From Trickster Wiki

Pet Leveling Basics

There are a few special pets (mostly from Egg Shop) that you can level up VIA growth. When a pet levels up, his name changes from T1, T2, T3, T4, his level increases along with his stats.

More about Pet Leveling

• You can NOT level normal pets, only pets that have a "T1, T2, T3, or T4" at the end of them!