Rock Smash shorthop lasers. If you manage to get in his face, you can go between Rock Smash (trades with Jab, gets set off by some aerials, beats spotdodge, great risk/reward), U-Smash (catches Falco before he can get a low laser off, can be done out-of-shield to beat Jab) and spotdodge (is relatively safe overall, gives you frame advantage if he rolls, can help you pressure Phantasm). If you get a grab, you can U-Throw and attempt to juggle (probably the best option) or B-Throw and try to pressure with another grab, a read on his roll, or Rock Smash his quick attacking options.
As Squirtle, crouch his lasers and be really patient. If you're smart about keeping yourself safe, he won't be able to land the B-Air he needs for the KO, so he will have to resort to unsafe Smash attacks. F-Tilt, D-Tilt, shellshift B-Air and grab. U-Throw if Falco doesn't have many platforms to work with, but F-Throw can help you follow up at low percents otherwise. Don't run into F-Tilts or B-Airs--Make him come to you at all costs.
As Ivysaur, you should probably just switch. If you switch on the edge of a platform, he'll have to settle for something like grab -> D-Air on Charizard, which isn't too terrible. If you have to, poke with D-Tilt and B-Air in order to keep him off you. Dash Attack can beat Phantasm if you space it well. Dash Attack and walk away -> F-Smash as a read are probably your most reliable KO moves, but neither are safe. If you manage to grab him, you can either throw him offstage with F-Throw/B-Throw (if the edge is close enough) and try to punish him when he gets off the ledge, or you can U-Throw and try to hit him while he falls. For when he's offstage, you can throw a Razor Leaf or RAR B-Air past the ledge to stuff his backward jump -> Phantasm attempts. If he jumps low, you can run off and N-Air/D-Air, but if you guess incorrectly, you're probably dead. If he tries to laser onto the stage, you can D-Tilt, B-Air, or F-Tilt to stuff it. Just try not to let his Phantasm go unpunished. For when you U-Throw him, either U-Air to beat an aerial or wait for an airdodge and F-Air him. These options are only useful if you're Ivysaur while Falco is at high percents. A Falco with little damage is pretty much impossible for Ivysaur to deal with.