Savestates is actually a serious hampering for Comix Zone. I've made the mistake of having a savestate where i've backed myself into a corner basically. :D
Ideal save times are at the beginning of each level, post hp potion, pre puzzles (Use the dynamite or Hercules for the fan) and before entering a double sized panel which usually means a series of fights or mini boss. Mercifully, the bosses are surprisingly easy compared to getting to them. Pro tip: panels where you can hang from something is a very good thing, the baddies tend to not be very good at landing hits on you when you're dangling and dual kicking their heads in. :)
Also, blockblockblockblockblock, jump kick are your friends. As is the kick combo which ends with a powerful high kick which slams them into panel walls.