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