Master Barf is weak to fire, so use that. Otherwise, a Multi-Bottle Rocket might be able to wipe it out in one blow. If not, use PSI Rockin, Paula's PSI Fire, and Jeff's best attacks.

For your defense strategy, Barf can cause nausea, and can also make everyone cry with a blask of stinky breath. Don't bother with Bash or Shoot attacks once you start crying.

Barf can call Slimy Little Piles into battle, but focus your firepower on Barf.

Once you've brought Barf's HP down enough, Poo will swoop down from the sky, hitting Barf with a blast of PSI Starstorm, which he just learned from the star master. This will end the battle, killing Barf.