Currently there are as many as 42 unknown/secret achievements for Bomberman Act Zero but here are the ones we know:
1,000 Bombs: Set 1,000 bombs.
Block Break 1,000: Destroy 1,000 soft blocks.
Kill 100: Eliminate 100 enemies.
Battle 100: Start 100 battles.
Battle Score 5,000: Get a Battle Score of 5,000 points.
Battle Royal: Kill 10: Defeat 10 people in Battle Royal mode.
Clear Round 10!: Clear up to round 10 in Single Battle mode.
Room Master: Create a room and fight a battle.