Didn't make it through the fight. But thanks to all the suggestions below I was able to set up another team with the Golden Civet, Amberbarb Wasp and a Cat with the suggested moves and we were victorious!
I strongly suggest a Golden Civet as the first pet (or something similar); mine was a S/S breed with Gnaw and Dive - it must be faster than the Cockroach. Use Dive as first ability - this way the Apocalypse will miss and you have a lot less pressure! (that Apocalypse is nerve wracking, if you ask me :D) And Gnaw does great damage to Critters too.
Awesome strat, I got 3 cockroaches, used dive on the first turn for each cockroach to avoid the apocalypse, Golden Civet almost soloed it, just had to bring in Mr Bigglesworth at the end to finish off the last roach.