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