Little Mac/ Falcon/ Sonic/Fox/Sheik
I can answer four out of five (the one I can't answer is sonic because it strikes me he's been made too fast that most attacks from most characters rarely land).
Falcon:
Easiest of the group actually (only one I consider 'fair'). During the initial match your first move should be de facto frisbee with shot (most Falcons rush). Fast but daft ones will shield at the frisbee (which gives you an opening). Competent ones will jump at the frisbee - which can be punished by a roll dodge and then frisbee again. If you know the Falcon you're fighting is likely to jump, deploy and rapid tap the can first (so as the Falcon jumps, he meets the can).
If a Falcon combo locks, mash the B button (which will deploy the can and break the lock). Immediately either neutral air (if they stay close) or frisbee if they go flying back. Distance is key. If a Falcon stays close, either roll dodge and light jab (you want the rapid attacking duck jab lock), or if he's a heavy shielder, roll dodge and grab, or if he's a spot dodger, roll dodge and frisbee with immediate shot. Once you interrupt him (jab lock, grab or frisbee), use the moments to calculate your next move - jab lock will allow a frisbee follow up (or if he jumps, can), grab with back throw will allow a frisbee follow up, and the frisbee a dash attack or forward air.
Avoid direct confrontations at all costs, even if it means excessive dodging, as Falcon is a 'power user'. Your mainstay will be roll dodges and frisbee interrupts.
Little mac:
At your own low percents, ledge camp and provoke using projectiles (if you're high percent, try to stay centre stage as his punches will launch you). Classically they will rush and do a side-B - punish with a well placed jump and back air and knock them off the edge. Most little macs won't anticipate this and will miss the narrow window for recovery. Those that do will barely grab the ledge. During this time, set up a can and drop it on them (regardless if they shield or don't) when they get back on. During the shield window, frisbee (most try to escape) then follow up with a dash (if they jump, forward air, if they don't, dash attack).
Example video (note I don't even use projectiles):
The issue you'll likely encounter is a running little mac is so low he goes under the frisbee. FB's window is very short: either at the end or near the beginning. Shots won't miss him, however. You'll need to rely on can deploys, which will stall little macs (either they will shield, punch the can or if you time the shot as they go past, get blown up by it). If they shield, frisbee, if they punch the can, dodge the rebound. Gunmen won't miss either, but their delay time is so slow you risk being punched in the running time.
You'll be heavily dependent on light jabs and rolls to space him. You can also use back and forward airs as mac's weakness is countering air attacks. Once he's off the ledge, either f-air or b-air him further out of his range. Be careful not to make the mistake of canning him near the ledge as it restarts his up-B (it's often safer to be less aggressive with the can when it comes to little mac off the ledge).
Another trick is to let him rush you near the ledge, dodge roll/shield the attack (dodge roll is better), toss off the ledge and b-air/f-air as appropriate. Little mac's greatest weakness is a lack of air time, so keep him over that edge.
Fox:
Against an extremely competent player, Fox is one of the hardest to beat. You can easily distinguish because a hardcore player will go close range and go for jab locks, an inexperienced one will immediately try to use blaster or reflector. They require different approaches.
If competent:
Fox requires roll dodges and light jabs, before frisbee follow ups (his attacks destroy frisbee, with the exception of his side-B which can be interrupted by a well timed shot). Very bizarrely, you have to fight him close combat and keep using light attacks (air jabs, neutral air, light jabs, jab locks) - you do not want to give him an opportunity to start an attack because once that occurs it will end in tears. Most foxes will down air on approach, so move to the side and either back or forward air. Once he's off the ledge and being juggled, different story again: you'll want to gunman/can/frisbee when he's off the ledge, and your goal will be to interrupt him off-stage often (his high gravity works to his disadvantage here). Done right, a gunman will interrupt fox fire and he will fall to his doom.
Once off the ledge, whatever you do, don't let him get back on. Even if the projectiles miss, use a dash attack and launch again. Keep the pressure up.
If incompetent:
At the start of the match, either:
Deploy gunman immediately to absorb the laser fire, or
Jump towards him and depending on your confidence, either land early and frisbee (it will override about 3 laser shots and fox takes time to put away his gun), or forward air him near point blank.
Provoke reflector by purposeful frisbee spam (you might provoke it by normal projectile tactics), your next move depends on his approach: if he maintains the reflector, build up his confidence with multiple frisbees before doing a sudden dash attack. If he uses it irregularly, use an obvious early frisbee to encourage reflector deployment and then dash attack or jump and forward air.
Shiek:
Probably one of the most annoying characters to go up against, of the zero suit spamus jump spam variety. Good news, beatable! Bad news; tricky.
Most shieks will start off with charging their needle spam barrage, which is your opening. Don't make the mistake of using projectiles, they won't reach (and the needles go through everything). The good news is the needles don't destroy the frisbee (the bad news is they still hit you). Jump to about mid-way and then frisbee followed by immediate shield and then frisbee shot on contact (done right, your frisbee will hit them as they launch their needles which will hit your shield).
Once hit, Shieks will often act confused and rush. Frisbee again, but this time follow up with a dash attack and an air attack after that as appropriate. They will likely start jump spamming to dodge frisbee - switch to cans and hit them in mid-air (if they dodge the can, either forward air punish or punish on defenceless landing).
Your biggest irritation will be the homing jump attack (why Nintendo, why? It's not a skill...). The good news is it can be foiled - by gunmen and cans (it will home in on gunmen instead of you in 9/10 cases). You can also 'shield and respond' (however Nintendo decided to reward homing spam by making shielding it bounce them to safety), but roll dodge and respond (frisbee is best) works better as Shiek will hit the ground hard with a few frames for opening.
The explosive up-B is rarely used aggressively, but the two variations are spot up-B (they up-B back to where they are to punish a dash attack) and aggressive up-B (they up-B to your location). Frisbee the first and 'shield and respond' the second. Whatever you do, don't try to attack in midair when they try to recover, but rely on projectiles. Done right, a can will force a premature up-B which will leave them open to another air jab.
Once you get used to the movesets - can for jump spam, frisbee at mid range for needles, roll dodge and respond for homing attack, shield and respond for up-B and get into dash attack and air attack follow ups, Shiek becomes easy to juggle and then clown.
Sonic:
The nightmare that most people hate. This is a character I do lose to, but it's mainly because I haven't figured the 'trick' to beating Sonic (his moves override most of duck hunt's moves, and his attacks are faster than the ones that don't). Incompetent ones are easy - stay near the ledge like little mac. Most will homing B or spin to their death.
All I can tell you is the homing B has the same vulnerability as Shiek's - if you roll dodge it rather than shield, sonic hits the ground hard leaving him vulnerable, but by the time you respond he's either shielding, roll dodging or attacking. Shielding the forward-B spin attacks seems to work well to stop attack locks to fatality, but as said, difficult to punish, so feel free to ignore me on that one.
vs. aMSa