Here is the full list of all 84 Warhammer 40,000: Dawn of War III achievements.
Complete the mission on Hard Difficulty
Complete the mission on Casual Difficulty
Complete the mission on Normal Difficulty
Great job! You completed the entire campaign on Casual difficulty.
You've put your knowledge into practice and conquered the campaign on Normal difficulty. Congratulations!
You've conquered our strongest challenge and completed the Campaign in Hard difficulty. Great job!
Level-up Elite to the max. Great job!