Here is the full list of all 37 King's Bounty: Dark Side achievements.
Train all the talents in your class tree (at least to level 1)
Win 25 fights without using the Spell Book
Organize a fan club
Collect 50 artifacts and items during one game
Open 100 chests during your travels
Get the achievements Bane of Life, Fighter, Butcher, Cool Warrior and Looking for Trouble
Win 25 fights without using Rage skills
Inflict 300,000 magic damage during one game
Get 15 medals (at least 1st level ones)
Receive 500,000 damage points in one game
Defeat 25 enemy armies in a row without replenishing your army
Destroy 100 enemy troops
Deal a total of 100,000 damage points
Lose 1,000 troops
Get the following achievements: Greedy, Collector, Heartless, Amateur Jeweler
Defeat the Spirit of Light in the final battle without using your Spell Book.
Get the ogre girl for your army
Raise your character to the maximum level
Complete all Magic Department quests
Collect any complete set of items.
Accumulate at least 10,000,000 gold
Complete the game with the Demoness class on Normal difficulty or higher
Complete all Military Department quests
Take 10,000 prisoners
Defeat the Spirit of Light before 10th round
Complete all Engineering Department quests
Collect all the 12 Great Artifacts of Netana
Complete the game on Impossible difficulty
Complete all Department of Experimental Weapons quests
Gather all the companions
Increase any 2 attributes of your troops to the maximum level
Get the achievements High Mage, Mad Courage, Reckless Fighter
Increase all improvable attributes of your troops to level 3
Complete all Research Department quests
Complete the game with the Orc class on Normal difficulty or higher
Get the Metamorph for your army
Complete the game with the Vampire class on Normal difficulty or higher