Bronze:

WHOMP WILY!
Objective: Clear the game once.

SUPERHERO
Objective: Clear the game on HARD.

WORLD WARRIOR
Objective: Defeat one of every type of enemy.

TRUSTY SIDEARM
Objective: Defeat the 8 bosses with just your default weapon.

NO COFFEE BREAK
Objective: Clear the game without using any energy, mystery, or weapon tanks.

Silver:

BLUE BOMBER
Objective: Clear the game in under an hour.

HARD ROCK
Objective: Make it to a boss room without getting damaged.

HEADBANGING
Objective: Defeat the 8 bosses without your helmet on.

DESTROYER
Objective: Defeat 1000 enemies.

TENACIOUS
Objective: Clear the game without continuing.

INVINCIBLE
Objective: Clear the game without dying.

MR. PERFECT
Objective: Clear the game without getting damaged.