This is difficult to accomplish without cheats because the two big cannons are next to impossible solo. What you need to do is buy 8 piercing shells from Pobre Obre and fire them at the beginning of the fight. There's a slight chance the big cannon won't be able to act afterwards, or at least only act, like, one turn out of 10. If he doesn't you're screwed, try again.
Getting past the mutant crocodile in the sewers was worse, seriously.
I got him with Concentrated Methyl, one of the prizes from the Devil's Tower's vending machines. Then I went and beat Mr Muscle with it too. (I couldn't do it before, the main character is really underpowered on foot)