Defeat the Bosses in the following order unlock and use the corresponding attack with the next Boss.

Sheep Man (use Mega Buster)
Pump Man (use Electric Wool)
Solar Man (use Water Shield)
Chill Man (use Solar Blaze)
Nitro Man (use Chill Spike)
Commando Man (use Wheel Cutter)
Blade Man (use Commando Bomb)
Strike Man (use Triple Blade)