Here is the full list of all 34 EvoMon achievements.
The base game contains 28 achievements, and there are 2 DLC packs containing 6 achievements.
Trained All Evomons in the game
Had your first Evomon battle
Your Evomon couldn't make it
Finished the Jungle Expedition
Finished the Mountain Expedition
Finished the Volcano Expedition
Destroyed 100 obstacles in the Expedition Mode
Ran away from the Expedition boss battle
Found a Secret Item in the Expedition
Made the first Evomon Fusion
Fished every fish in the pond
Your Evomon got filthy
Used your first potion
Your evomon reached the last evolution stage
Finished all the Arenas
Found the secret Evomon
Found the most powerfull Evomon
Hatched your first Evomon
Collected 100 Evocoins
Collected 1 Evocoin
Expedition Failed
Hatched 30 EvoEggs
Restored your first Evomon through a DNA string code
Trained the rare Pitayamon
Entered the store but didnt purchased anything
Froze your first Evomon
Trained the rare Hacumon
Trained the rare Roimon
Played the gacha machine 100x
Found the luckiest Evomon
Found your First Ara Evomon!
Found every Ara Evomon in game
Made the first trade on the Evotrade
Made 30 trades on the Evotrade