Here is the full list of all 10 10 Minute Barbarian achievements.
Killed more than 1200 enemy in one mission
Own 10 Trees
Got 1200 of your own troops killed in one mission
Victorious in the Northern Wastes
You made it through the intro.
Got 4 dragons
Won a Queen's Guard award for an amazing score
Hired a Necromancer
Saved the world in your own particular...idiom
Beat every mission as Lord High Emperor