Here is the full list of all 27 AK-xolotl achievements.
Unlock everything from the Small Paw's Dealer Shop
Unlock everything from the Droppin' Doggo Shop
Win 10 runs
Unlock everything from the Blisstaker Shop
Die 100 times
Defeat the Mimic for the first time
Win a run for the first time
Defeat all the enemies (not counting bosses and special enemies) at least once
Unlock 8 Primary Weapons
Defeat 1000 Caterkillah
Defeat the Fish & Chipz for the first time
Enter a secret door for the first time
Collect 500 Doraditos in a single run
Absorb the Happiness of an Axolittle for the first time
Roll 537 times
Defeat the Sock it Snake for the first time
Defeat 25 Frogs
Grow your first Axolittle into an adult
Complete a Challenge Room for the first time
Defeat the Hell' o Kitty for the first time
Break Chipzs bucket for the first time
Defeat the Pond Pincer for the first time
Drop an Axolittle baby near the cauldron
Spend any amount of gems for the first time
Collect your first egg in the game
Die for the first time
Enter a run for the first time