I really challenged myself to figure out a way to level pets on these 2 troublesome sprouts and I finally had some success.
Scalded Basilisk Hatchling: 2, 2, 1
Tiny Blue Carp: 1, 2, 1
Any level pet with hp <1465
Start with Scalded Basilisk Hatchling.
Round 1: Stun
Round 2: Thrash - He will switch pets to the king at this point.
Round 3: Feign death - This makes him miss Fist of the Forest and switches you to Tiny Blue Carp.
Round 4: Pump, pump, pump, pump - For some reason I never saw him use Righteous Inspiration while I pumped him into the ground.
Round 7: Wild Magic - Get this off before you take a Fist of the Forest to the face and your carp dies.
Switch back to Basilisk
Round 8: Thrash - He will sometimes use Righteous Inspiration here, no problem if he does.
Round 9: Thrash
Round 10: Stun - Seems to usually use Righteous Inspiration here
Round 11/12: Thrash
Round 13: Feign death to avoid Fist of the Forest. This automatically brings out your leveling pet
Round 14: Quick switch back to basilisk
Round 15/16/17: Thrash, Stun, Thrash
This Strategy is not crit immune, infact 1 crit from King and your toast. It some some durability against RNG, so don't worry if your thrash sucks.