Alright folks. I was too lazy to see how much of the Mewtwo match-up was on here, so I'm gonna copy paste something I posted elsewhere here. (Since it's the best place for it)
Note: This far from comprehensive, but it's a good starting point to learn the matchup.
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VS. Mewtwo:
Pros: DK can punish Up-B incredibly well, and has the power to put an early end to Mewtwo. Plus, while Mewtwo is floaty, he's still medium weight, giving your throw combos excellent potency in the match-up.
Cons: Mewtwo can simply outspace DK with relative ease. A wise Mewtwo will not warp spam against a DK who can punish it, they will resort to a defensive game to get you to approach carelessly, and safely build damage with his tail. DK's size makes him incredibly vulnerable to F-Air, and Mewtwo can warp above DK's recovery for an easy Meteor punish.
How I feel the match-up slides: Personally, this tends to be in DK's favor. However, I will write like you're fighting more competent foes, the kind that can still make this their match-up. For an overall scale, I feel 65-35 DK's favor.
Defense is much more important in this fight, so I'll discuss that first.
Defense: Climbing the "Warp"ed Wall.
Mewtwo has a very fast and very high pressure offensive game. With good space on aerials and good frame data, defending against Mewtwo requires thought and patience.
Step One: Stay Grounded during Neutral game.
I cannot stress that enough, the ability to simply guard Mewtwo's aerial approaches is devastating to the pressure which he can apply. It forces him to go for a warp side B- approach, or to back off and try to apply pressure with Shadow Ball before warping.
The shadow ball warp approach becomes easy to read once you've seen it a few times, and running in and power shielding it usually throws off Mewtwo's approach in one of two ways.
Scenario One: SB hits Mewtwo.
What are you waiting for? Now's your chance! Go for dash attack, or if time permits, grab him, and let the fun begin.
Scenario Two: SB misses, and Mewtwo warps.
If you ran toward Mewtwo and power-shielded, it's more than likely you ran past his intended warp point, watch out for a b-air from warp. When he misses an aerial and has to land from float, go for a punish. (I'll describe best practices for that later)
Countering basic warp approach
Mewtwo's bread and butter. Warping is a devious, yet, simple approach in Mewtwo's arsenal. In most cases: A better Mewtwo, even if he doesn't warp straight at you, will come out swinging IMMEDIATELY. Mewtwo's learn to throw out hitboxes to protect themselves from being punished whilst warping. It's good Mewtwo practice, but DK has ways to cope.
Imagine this scenario:
Mewtwo warps. He was too far away in front of you to warp behind you, and you're at relatively low percent for F-air kill. This means he'll probably warp above, and falling N-Air. Remember, unless Mewtwo aims for the ground, he has to travel the full distance of his warp in the direction he choses. So with some practice, you know exactly where he'll end up. If he goes for the overhead, simply jump so you're overlapping where he'll spawn, and make him eat a Nair. Sure, you'll probably trade. But your Nair vs a hit of his Nair is a great trade. If you want a more combo set-up options, try learning how to punish with Up-Air. It's more precise on the spacing, (since trading will nullify the use of a combo set up move like Up-air, leaving Nair as the better option if you're not sure of yourself) but hitting it without trading leads to follow up potential.
Now look at this scenario:
Mewtwo warps. He made a note of getting closer before he did, and once again, he can't shorten the distance of warp unless he lands (which has lag) so he's probably trying to get behind you for one of two approaches.
A: He wants a few quick hits, and doesn't know how much you like to guard yet. So he will probably B-Air wall. Power shield one, and you can jump out of shield Bair to punish in between two of his Bair's (takes some practice, but not too hard)
B: He's aware you might be expecting Bair, and knows you know how to defend yourself, expect a side B from behind. Harder to dodge, but it's simple really. Simply walk forward, and whilst in his animation (which has some vulnerability) jump Bair. (You have to lean into this a little, because Side B has pushboxes)
For both, don't stop there. L_cancel, and make him keep eating your own B-Air wall. A good sour spot bair can set up for a grab, but it's more technical.
Final Scenario.
Mewtwo warps, and you're at high percent. He's the same space from the first scenario, so no flanking you. He'll try two things.
First: A direct frontal assault. He'll come at you at ground level (not touching though) and F-air. You want to shield this approach if you know it's coming. Harder to punish, since a good Mewtwo will retreat Fair in order to prevent a punish. DK has a harder time air punishing right in front of him, especially in the time provided. Also, if you don't power shield, you'll be in stun too long to punish this option if they retreat. The plan is to be patient. Wait for them to get too ambitious. If they flank you with another warp after the first fails, you know how to punish already. (Once again, harder to punish Fair, but much more punishable if they come from behind) Note: If you see this approach coming, you can try turning around and shielding it, so your back is to Mewtwo. Giving Bair a time to shine. Also, if they fair and don't retreat. Make the sonuva' gun eat a Nair. Chicks dig Nair.
Second: He may try to come from above and Dair to pop you up. Like the Fair approach, this can be done in retreat, but the cool down if Mewtwo stays in the air is long enough that either Nair, UAir, or Bair will punish. (depending on how Mewtwo retreats) As always, shielding is excellent to block. Counter however you see fit.
"But Akashic! I missed the punish! Now what?!"
Step One: Don't panic. Remember? He has to land. A good Mewtwo will always get his L-cancel while landing, so he won't be vulnerable long, but he will be vulnerable. If he's retreating before landing, approach with a walk, and F-tilt the landing. (This is the safest way, you can get creative after you learn to punish it more consistently) If he gets ambitious, he'll probably, follow-up whatever approach with Nair. Fun Fact: The shield lag on Nair is negligible. Punishing afterwards is an option. (Or, if you want "shock" value you can grab between the hits on Nair, it's hard, but possible)
"What if I miss all the chances to punish!?"
Stay clam. If you're confident in your spacing, close the gap and keep him in range. (Watch for grab here) If you're not feeling so bold, retreat with wavedash (a roll could suffice, I do so a lot) And wait for him to try again.
Moving on:
Air defense: Surviving the onslaught
Bad news: Mewtwo outsmarted you. Maybe he used Side B, and you ended up above him. Worse case scenario, he's gonna give build up percentage, and rising Fair you. But only if you panic. Remember, in the air, you are most vulnerable to being juggled by Mewtwo from his behind (Bair) and from his front diagonal (UAir). He can get you from his direct front (Fair) but it has much less range. The tl;dr of defense here, is to watch these key areas and avoid them in falling, but I will go into some detail ahead if you want.
Directly above Mewtwo: Tl;dr Dair
Mewtwo will go for U-Air, this much is obvious. If you have enough space between the two of you, a dair can end his combo ambitions, even with a trade. You can air dodge through him if you feel fancy, and fast fall to ground. If you can get to his front-side. (Note this applies to EVERY air scenario with this opponent) NAir or Bair depending on what side is facing him.
Behind Mewtwo: The worst nightmare. tl;dr Bair, Nair, Up-B dodge
Mewtwo's Bair will end you if you can't dodge it. Your best bet is if you know you can't dodge, go for a trade. Nair works with timing. And Bair rivals it's range well. You can also Up-B THROUGH him if you feel lucky. (This also racks on some nice damage, good for you) Remember, once you break the juggle, return to earth ASAP
General Practice in the Air: Up-B: The secret trump card.
Regardless where you end up, Up-B is usually a solid option to escape. It's got faster horizontal movement than Mewtwo so it can juke him. It's got solid frame data, so you can also challenge him with it. (Mentioned above)
Final Note about Aerial Mewtwo: He has to land.
He floats, he doesn't fly. He has to come down at some point. Keep it in mind when determining which option is right for you. Once again, if he warps, he has to travel the full distance in that direction. So go for a juke if he goes to comeback. If you're not in hitstun, throw a Nair like I mentioned earlier in countering warp.
WHEW. Defense in a nutshell there..... Nah, just kidding. I've nearly forgotten the most important part.
Defense against the patience Pokemon: Fighting the tail.
Imagine: You're fighting a battle hardened Mewtwo. He knows you can punish warp with your aerials. So he'll be patient. Knocking you away with his tail and firing shadow balls. What do you do?
The better question is, what can you do? This is where Mewtwo gets his 35 points in this match-up. A good approach here is hard, and it's better to try to debunk all of his crap and wait for an approach of his own. Instead of imagining scenarios, I'll just remind you of some of your weapons.
Dash attack has armor. If you read a tilt, go for it. Worse case scenario: You trade.
Powershielding reflects Shadow Ball. Learn that timing folks. Then follow up.
And that thing you always forget about, Down B. This forces him in the air, and when you're below Mewtwo, you're at the advantage.
RAR Bair is fast, and can punish if he makes a commitment on the ground that keeps him there. It also nullifies poorly charged shadow ball.
There's more, but it this should help get your mind flowing in the right direction. The biggest part about defense in this matchup is being able to play it by ear. (or, in different terms, play it as you go)
Offense: Can't catch pokemon til you weaken them first!
Mewtwo is incredibly weak to DK when Dk is below him. U-Air juggles well. And Grab combos devastate Mewtwo. When you've made Mewtwo go above, switch gears, and go ham.
D-Tilt and Crouch Cancels. Crouch cancelling is vital to fighting Mewtwo on ground. And it can be followed quickly by D-Tilt, which rivals Mewtwo's range. Get in close, crouch the tilt, punish. Watch for grabs here, they'll devastate you.
Up-tilt. Up-tilt is a solid option once Mewtwo is above you. It allows you to stay grounded while juggling him at low percents, and can guard the aerial approaches with ease.
If Mewtwo ever rolls (it does happen) remember that it has WAAAY more distance than most rolls, and he'll probably do this to dodge a tilt and get behind you. Despite it's range, his roll has some bad ending lag, jab or tilt to respond.
Combos: Jab (both hits) into D-tilt hits Mewtwo at fairly early to decently high percent (0-65%) Depending on how he DI's, you can follow with insta Nair, grab, or dash attack.
Forward Cargo throw combo: Even with good DI from about (50-80%) this should land. (For the uninitiated, Grab->Cargo->Jump Forward->Forward Cargo throw->Double Jump-> Fair) At lower percents, you can forgo the double jump and Nair him. If you pull this combo at 80, you can kill Mewtwo on some maps.
Up-Cargo: The bread and butter. Like with most foes, low percent leads to Up-Air juggles. At high percent, you can buffer a Fair from your throw (after a double jump) and land the wild haymaker.
Reverse Cargo throw has some utility, try to follow with up-air or Fair.
If you grab Mewtwo from too high of a percent for combo, you can choose to kill him with back throw, or up-throw him to get stage control.
Aerial Side-B Meteors don't affect Mewtwo much, but can be used if he's going to warp to ledge for a sweetspot. (Only the first time, the warp from ledge to ledge warp has full invincibility, so don't approach)
Giant's Punch: Keep one charged. Once you better read warps, You can punish big time.
DK-cide: Always a punish option that is effective based on the player your facing and less the character. Try to see how much they mash when you grab them before you show this hand to the opponent, since if they mash, they are bound to live (ESPECIALLY Mewtwo) and you're bound to die horribly.
F-Air. This move is excellent for spacing Mewtwo while he's in the air. Like with Giant's Punch, you can use this to punish warp big time once you get a feel for how he warps. This can be used to challenge Mewtwo's juggle too, but usually to less effect.
TL;DR. Block warp stuff, punish it big. Combo the crap out of him when you can. Don't miss opportunities to take stocks. Play patient, and don't forget your whole arsenal.