Here is the full list of all 29 Battle Sweeper achievements.
Finish a level without fighting any monsters
Drink a Potion
Drink 5 Potions
Drink 10 Potions
Kill a monster
Kill 5 monsters
Kill 10 monsters
Kill 15 monsters
Kill 20 monsters
Reach level 5 with the Knight
Reach level 10 with the Knight
Reach level 15 with the Knight
Reach level 20 with the Knight
Reach level 5 with the Rogue
Reach level 10 with the Rogue
Reach level 15 with the Rogue
Reach level 20 with the Rogue
Reach level 5 with the Lizard
Reach level 10 with the Lizard
Reach level 15 with the Lizard
Reach level 20 with the Lizard
Reach level 5 with the Wizard
Reach level 10 with the Wizard
Reach level 15 with the Wizard
Reach level 20 with the Wizard
Reach level 5 in Classic Mode
Reach level 10 in Classic Mode
Reach level 15 in Classic Mode
Reach level 20 in Classic Mode