Bakufuu Sentai Bombermen

The goal of each stage is to destroy all enemies on the map, and find the exit warp hidden beneath a random soft block. However, the game's focus is mainly about high scores, displaying prominent score boards highlighting each stage's fastest time and highest score. You are given 3 minutes to complete each stage, and running out of time will kill the player. Bombing the exit spawn up to 5 enemies.

The game can be played with one of five characters and is split into two modes: Classic Area is very much inspired by the original NES game and features 5 stages, all with very basic enemies and gimmicks. All five characters play identically in Classic Area.
Completing Classic Area will unlock Arrange Area for the chosen character; you must complete it with all five members to make them accessible in that mode.

Arrange Area boasts more dangerous foes, unique stats and abilities between characters, and 9 stages. Each character possesses a Special Skill that can be used any time by pressing the X Button, and a Super Bomb: detonating a bomb will fill a gauge on the upper-right. When it is full (after 10 detonations) you can unleash a Super Bomb with the L Button; its effects are different from character to character. Up to 3 Super Bombs can be stocked.
Completing all 9 stages with all five characters will unlock the Boss Stage for all characters, with a different opponent for each player. The game is completed once all bosses have been defeated.

Challenge Mode

Details on the Challenge Mode can be found here.

Multi Mode

[i know nothing!]

This game boasts a game-sharing functionality - so long as two or more people own a copy of this game, I.Q. Mania or XI Colloseum, you can play multi-player matches in any one of the three games.
... but since you can't play multi-player with only one PSP, I can't comment. Welp!

Extra

Five mini-games can be found under this menu, and using the game-sharing functionality, can be played in multi-player so long as other players own either this, XI Colloseum or I.Q. Mania can be played in multi-player as well. Alongside demos of the aforementioned games, XI Collo Bowl / XIコロボウル and Mah Jong / 麻雀 are also available to play.

controls

If the player dies, all items are lost (except for Fire Ups, Bomb Ups and Speed Ups). All items are lost if you change game mode or player character. Be aware that enemies can collect items, and there's no way to get them back!

Fire Up / ファイアーアツプ

Increases bomb blast radius by 1. Maximum of 6.

Bomb Up / ボムアツブ

Increases bomb stock by 1. Maximum of 8.

Speed Up / スビードアツブ

Increases movement speed by 1. Maximum of 9.

Bomb Kick / ボムキック

Allows the player to kick bombs by walking into them. Press Triangle to stop a bomb in its tracks.

Power Glove / パワーグローブ

Press and hold Circle on top of a bomb to carry it; release Circle to throw it 3 tiles ahead.

Punch / パンチ

Press Square to punch a bomb in front of you; bombs travel 3 tiles ahead.

Line Bomb / ラインボム

Press Square to lay all your bombs in a line straight ahead of you.

Boyoyon Bomb / ボヨヨンボム

Jelly bombs. Thrown bombs will bounce erratically before settling; kicked bombs will bounce right back if they hit an object.

Penetration Bomb / 貫通ボム

SINGLE PLAYER ONLY. Bomb blasts will penetrate through soft blocks.

Customize Accessory / カスタマイズアクセサリー

SINGLE PLAYER ONLY. Has a random chance of dropping from an enemy in Arrange Mode. Collecting one will add a costume piece to your collection; you can access these under Options > Character Customize.

Skull / ドクロ

MULTIPLAYER ONLY. Inflicts whoever collects it with one of the following curses:

Devil / デビル

[i've no idea what this does until i can get multi-player working!]

Red Bomber / レッドボンバー

Special Skill Soft Block Punch: Pressing the X Button will allow Red to punch a soft block, pushing it forward until it hits an obstacle. Only works if there's empty space on the opposite side!

Super Bomb Red Bomb: Lays a transmitter that summons missiles to rain down, creating a 5x5 square of flame.

Blue Bomber / ブルーボンバー

Special Skill Super Dash: Hold the X Button to increase your movement speed.

Super Bomb Blue Bomb: Lays a bomb that looks identical to a soft block.

Yellow Bomber / イエローボンバー

Special Skill Line Bomb: Press the X Button to lay all your bombs forward in a line.

Super Bomb Yellow Bomb: Lays a bomb that takes 8 seconds to detonate.

Green Bomber / グリーンボンバー

Special Skill Bomb Kick: Press the X Button to kick a bomb if it is in front of Green. Be wary that the wind-up and recovery animations are quite long.

Super Bomb Green Bomb: Lays a lightning bomb; its explosion will linger for longer than usual.

Pink Bomber / ピンクボンバー

Special Skill Jump: Press the X Button to jump into the air; pressing it while moving will make Pink jump 2 tiles forward, over bombs and obstacles.

Super Bomb Pink Bomb: Creates a forward-facing explosion in front of Pink that spans 8 tiles.