Here is the full list of all 14 Might & Magic: Clash of Heroes achievements.
Reach Level 10 in online multiplayer mode
Win a battle in 1 vs. 1 online mode.
Win a battle in 2 vs. 2 online mode
Complete all main quest and side quest objectives in all Campaigns
Reach a Hero level of 10 and max out all units to level 5 in any Campaign
Complete all Battle Puzzles in each Campaign
Complete all bounty side quests
Collect all artifacts of each single player campaign
Unlock all special units
Create a link of 5+ formations in battle
Triple fuse an attack formation in battle
Win a battle in the Sylvan campaign
Win a battle using any of the playable Villain characters.
Deal an additional 100HP of damage to the enemy Hero on the finishing blow.