Here is the full list of all 8 Drill Arena achievements.
Don't use bonuses the whole match
Win one match in singleplayer mode
Win one match in multiplayer mode
Win 10 times in any mode
Survive whole match without losing all health
Destroy every type of robots in one match
Destroy 3 opponents in one use of hyper mode bonus
At the end of the match there was not a single block left on the field