I got bored using snails and found my 2 Emperor Crabs to be the quickest way to get through Zusshi. Breeds probably don't matter here but I happen to have leveled P/P and H/H; here's how I use them:
P/P Emperor Crab: Whirlpool, Healing Wave, Surge til Elemental is dead.
Swap to H/H Emperor Crab: (Snail's healing attack is weak v. Aquatic which is a nice perk.) Shell Shield, Healing Wave timed to hit after Dive hits me, Snap til Snail is dead.
Between the two crabs they have plenty of health left to take out the Bug; your leveling pet only needs to be in for one round. If you time Shell Shield on the second crab so you still have Acidic Goo but no shield on you when the Snail dies, you'll be damaged during the Drowsy round and won't be put to sleep.
Now if only I could also time it so I never ever have to fight that stupid mob that wanders across Zusshi's path.