Well, since this is where we're going to talk about the match up, i guess i'll start off with what i know. What i'm about to say is what i've gathered from many Greninja encounters and mostly from my recent encounter from a great Greninja (goes by name "Deadly Shoc") who really knew how to pressure and react fast, and space me out. I'm gonna talk about dealing with this match up in 2 sections, one on how to edge guard/deal with him off stage, and the other for how to deal with his specials and smash attacks.
When it comes to edge guarding Greninja, this is what will typically happen when you get him off stage and this situation is now possible. Depending on the skill/position of the Greninja, he'll either:
A) While coming in from High/Lined up with the edge, they may use Shadow Sneak mid air to recover on the stage and try to reach the ledge in order to get on stage a good distance away from the edge or keep you from edge guarding them
B) Fast fall and move horizontally in the air, then use Hydro Pump to reach the ledge
If they go with A, something you should know is that should they happen to line up the attack with the Ledge, and you're at the ledge, they'll hit you (this is easy to shield of course), and be free to hydropump directly upwards onto the ledge (unless you can stage spike them, which doesn't have much of a long enough time frame to pull off even if you shield the attack and they instantly use their Up Special. You can use Vision to counter it if you time it right, but you'll want to not use forward counter, because then it will completely miss due to its hitbox being behind Shulk, though i've never pulled this option off before. They could also use the attack high enough in the air and teleport past the ledge at the height in the air that they used the attack and fall down onto the stage, and if you're quick enough, you can punish them for this, depending on how far they teleported.
For Option B, typically you can block this with Fair/Nair (or spike them), but it's risky with Greninja's Up Special as his is well known for being great for pushing opponents off stage when they try to recover and lead to a stock loss, so when trying to do this, you'll definitely want Monado Jump activated to improve your chances of recovering should you whiff/mess up the edge guarding attempt.
Now for battling him in general. From my experiences, i find it best to stick with Monado Jump and Speed for most of the match, a good Greninja can utilize their speed over Shulk and basically null Monado Buster's buff by pressuring Shulk enough so he can't land a hit/counter the assault. With Jump and Speed always active, Shulk has an easier/better time of keeping up with him and combating him effectively.
Greninja's grabs are pretty useful and are great for being pivoted, a useful follow up combo that Greninja's tend to use is U-throw into Uair, so be prepared for that. His tilts are ok, but not really much to worry about honestly. His aerials are also good, Uair is like Sheik's as it hits multiple times, Back Air is pretty fast and does 3 hits, Nair is...kind of weird IMO, doesn't do much damage and is a bit hard to land in my experience using Greninja, Dair is a stall and fall and unlike Toon Link's which has a windbox that you need to shield in order to avoid it and punish, it has no windbox which makes it easier to punish, although it like Erico says, it has to be Forward Countered in order to hit as Greninja bounces off Shulk should he land the hit. Last is Fair, which is pretty strong and his best attack for KOing in the air, it comes out a bit slow, but a good Greninja will be able to time it right, and it can be deadly.
His Smash attacks are good, D-Smash is good for punishing rolls, F-Smash has a good amount of range given that it's a "Water Sword", and U-Smash basically forms an arc around Greninja from above and to the sides, the most damage dealt from the top of the arc. His specials are different from what you'd face from alot of the roster. His U-special, Hydro Pump, can use be used on the ground in a left to right direction to try to blow you off stage, but if you stick with Speed/Jump to avoid/minimize it's effects, you shouldn't have to worry about it. Plus it has a pretty short range when used like that anyway. Water Shuriken (Neutral Special) isn't that hard to dodge/block, and it can't be saved which is good for us, but i wouldn't recommend just standing there and shielding a fully charged one, since Greninja can take the opportunity to grab you while you're shielding as you're left defenseless from blocking the attack. Also, like Erico said above me, you can take the opportunity while the attack charges to jump over Greninja and use Back Slash's initial jump to evade the attack and land the hit.
Shadow Sneak can be hard to see coming on dark stages, or if used when Greninja's right next to you, but more often than not, Greninja's will use it as an approaching option. Keep in mind, when they use this attack they always Walk when aiming it and cannot dash, so that can be a give away. I wouldn't recommend using Vision and just Shield the attack and follow up with a punish, since it's hard to tell when the Greninja will use the attack, and what direction it'll come from (Greninja can still hit you with the attack if they appear behind you, it does a different animation to attack if this happens and it will hit you), so you can easily mistime the attack or whiff. Last is Greninja's counter, which basically has more or less the same animation like Lucario's, but with Greninja, the Counter attack can come from 3 directions: Left, Right, or from Above (though this one isn't that safe). Since it's like Lucario's, the counter isn't instant nor traps you so you can't escape the attack like the Swordsmen, so it's easy enough to shield or sidestep. I do not know what affects the damage output of this counter though.
My advice is to basically stick with your M-Artes that improve your manueverability (AKA Jump and Speed) to keep up with Greninja's speed and attacks and not be overwhelmed. Shield is also good for surviving at higher percents, Smash is still good for when Greninja's at high percents and his KO moves aren't all that fast or easy to land, at least not outright/immediately. I would by wary of using Vision, as alot of Greninja's specials are hard to land counter with, mostly use it against his Smash attacks/tilts, and try to take advantage of your range to keep Greninja from getting in too close and pressuring you. Also, when trying to edge guard, definitely use Jump so you have a better chance of recovering should you get blasted with Hydro Pump, plus the speed/manuevarability is useful for landing off screen KOs before the enemy can use their recovery moves.