Here is the full list of all 14 Burg Battle achievements.
Win a battle
Win a battle against another player
Win a battle with only an altar
Kill 300 units
Kill 1000 units
Level up humans to 50
Level up hellspawn to 50
Get to wave 10 in horde mode
Get to wave 20 in horde mode
Get to wave 30 in horde mode
Add a talent point to the last talent in a tree
Complete the controls tutorial
Complete the gameplay tutorial
Win a game in less than 5 minutes