Accomplish the indicated achievement to get the corresponding number of Gamerscore points:

1,000 Bombs (5 points): Set 1,000 bombs.
Block Break 1,000 (5 points): Destroy 1,000 soft blocks.
Kill 100: Eliminate 100 enemies.
Battle 100 (10 points): Start 100 battles.
Battle Score 5,000 (10 points): Get a Battle Score of 5,000 points.
Battle Royal - Kill 10 (5 points): Defeat 10 people in Battle Royal.
Clear Round 10! (10 points): Clear up to round 10 in Single Battle mode.
Room Master (10 points): Create a room and fight a battle.

Additionally, there are 42 secret achievements:

10,000 Bombs (10 points): Set 10,000 bombs.
100,000 Bombs (30 points): Set 100,000 bombs.
1,000,000 Bombs (50 points): Set 1,000,000 bombs.
Battle 1,000 (20 points): Have 1,000 battles.
Battle 10,000 (30 points): You have had 10,000 battles.
Battle Score 10,000 (10 points): Reach a Battle Score of 10,000 points.
Battle Score 50,000 (20 points): Reach a Battle Score of 50,000 points.
Battle Score 100,000 (30 points): Reach a Battle Score of 100,000 points.
Battle Score 1,000,000 (50 points): Reach a Battle Score of 1,000,000 points.
Battle Royal - Kill 30 (20 points): You have defeated 30 people in Battle Royal.
Battle Royal - Kill 50 (30 points): You have defeated 50 people in Battle Royal.
Battle Royal - Kill 100 (50 points): You have defeated 100 people in Battle Royal.
Block Break 10,000 (10 points): Destroy 10,000 soft blocks.
Block Break 100,000 (30 points): Destroy 100,000 soft blocks.
Block Break 1,000,000 (50 points): Destroy 1,000,000 soft blocks.
Kill 500 (20 points): Defeat 500 opponents.
Kill 1,000 (30 points): Defeat 1,000 opponents.
Clear Round 20! (10 points): Clear 20 screens in Single Battle mode.
Clear Round 30! (10 points): Clear 30 screens in Single Battle mode.
Clear Round 40! (10 points): Clear 40 screens in Single Battle mode.
Clear Round 50! (10 points): Clear 50 screens in Single Battle mode.
Clear Round 60! (10 points): Clear 60 screens in Single Battle mode.
Clear Round 70! (10 points): Clear 70 screens in Single Battle mode.
Clear Round 80! (10 points): Clear 80 screens in Single Battle mode.
Clear Round 90! (10 points): Clear 90 screens in Single Battle mode.
Room Master 10 (10 points): You have created rooms and fought 10 battles.
Room Master 100 (30 points): You have created rooms and fought 100 battles.
Secret Panel 1 (10 points): Obtain Secret Panel "B."
Secret Panel 2 (20 points): Obtain the "Bomberman?" Secret Panel.
Secret Panel 3 (30 points): Obtain the "Diggerman?" Secret Panel.
Secret Panel 4 (40 points): Obtain the "16-Shot" Secret Panel.
Secret Panel 5 (50 points): Obtain the "Uhi-Uhi" Secret Panel.
Special 1 (20 points): Win without obtaining any Power Up Panels.
Special 2 (5 points): Play with both male and female frames.
Special 3 (10 points): You have played using all of the characters.
Survival Time 100 (50 points): Clear Single Battle mode within 100 minutes.
Survival Time 150 (20 points): Clear Single Battle mode within 150 minutes.
Survival Time 200 (10 points): Clear Single Battle mode within 200 minutes.
Draw 100 (5 points): Die 100 times to time-up draws.
Pressure Block 100 (5 points): Get crushed to death 100 times by pressure blocks.
Self 100 (5 points): You have died 100 times to bombs you set.
You reached the Land of Despair (50 points): Single Battle mode is all clear! Get back to the surface!