A GOOD strategy is to wait for stages that cause a lot of CPU SDs. Try to pick 1v3 matches on stages like Fourside (Pichu), Jungle Japes (Young Link), and Brinstar Depths (Ganondorf).
Fourside - Have everyone follow you to the left side of the stage then retreat to the right. Grab the left edge of the rightmost building. Most characters will try to hit you with a falling aerial. Right before they attack, press L or R to roll. Usually they don't survive unless they have good recovery.
Jungle Japes - Similar to the above. Hang on the edge of the center platform and wait for falling aerials from CPUs. Be cautious of Klaptraps. One hit and it's over.
Brinstar Depths - Stall for a bit then head down to the floating rock at the bottom right. Try to keep them off until it rotates. After the stage rotates, try to force them to get stuck on the rock and accidentally Up B off.
Other good stages are ones that are really big, like Temple. Try to eliminate characters like Peach on the 1v1, as heavyweights are really annoying on the 1v3.
Another tip is don't go to enemies, let them come to you.
Other tidbits:
Brinstar - When lava begins to rise, CPUs tend to do nothing but stand on the top platform.
Great Bay - CPUs only travel one end to the other by walking over the large platform. Go back and forth from the floating rocks while attacking from underneath. Or wait for them to fall and use a smash.
Onett - Try to throw them off or have all the CPUs get hit by a car at the edge.
Rainbow Cruise - Hang on the left edge, fall off, grab it again. Keep doing this until Mario does his F-air and SD.
Venom - Eliminating Falco is pretty easy if you can get him under the bottom wing. Keep him off every time he attempts to recover with Fire Bird.
Mewtwo - SDs a lot on 1v3 if CPUs push him off an edge while he's charging a Shadow Ball.
Ganondorf - In early versions of SSBM, he'll Up+B off the edge of a stage if he tries to intercept you.
Captain Falcon - Go near an edge, let him grab/throw you, then watch him Raptor Boost off. Hard to do on Mute City though.
You should be able to do this with a main with a lot of retries. Not to brag, but with a lot of luck, I was able to finish Very Hard All-Star with Pichu using only 3 continues.
