Snowshoe rabbit: play around with flurry spams a burrow maybe a dodge to kill 1st pet
2nd pet: u are switched to one of the snails: acidic goo -> ooze touch -> ooze touch. the dot from acidic goo killed him after this for me, my snail that got switched in was 292 attack power.
3rd pet: try to get acidic goo on it, no bigge if it dies tho. New snail: if acidic goo is applied, get ur ooze touch to hit it. if not: acidic goo -> ooze touch (if the tick does not crit u, u should be able to get 1 ooze touch in). Your snail dies, and now you switch back to the rabbit to finish it off. use dodge or burrow accordingly.
Zyalura and Satcomer are right. A couple of replacements needed, despite strat saying "any" breed will work. SS Brown Rabbit in place of Noblegarden Bunny (which I don't have), BB Rapana Whelk instead of SS, and Scooter did not have much work left to do.
I couldn't kill Lilly with any of the rabbits I have so used a Pygmy Cow. Stampede and Udder Destruction works every time. However the snails still proved troublesome as well but after a few tries with bad RNG I finally got it along with my Family Battler achieve!