Here is the full list of all 14 Might & Magic: Clash of Heroes achievements.
Win a battle in 1 vs. 1 online mode.
Win a battle using any of the playable Villain characters.
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
Reach Level 10 in online multiplayer mode
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 2 vs. 2 online mode
Win a battle in the Sylvan campaign
Deal an additional 100HP of damage to the enemy Hero on the finishing blow.