Most bosses in Megaman X8 have a certain weapon they're weak against. By using these weapons against them, you can deal more damage per attack.

Boss's name - Weapon
Optic Sunflower - Bamboo Pandamonium's weapon
Dark Mantis - Optic Sunflower's weapon
Gravity Antonion - Dark Mantis's weapon
Earthrock Trilobyte - Gravity Antonion's weapon
Gigavolt Man-o-war - Earthrock Trilobyte's weapon
Avalanche Yeti - Gigavolt Man-o-war's weapon
Burn Rooster - Avalanche Yeti's weapon
Bamboo Pandamonium - Burn Rooster's weapon
Vile - Avalanche Yeti's weapon
Fake Sigma (in Gateway) - Dark Mantis's weapon

Although Axl also has weapons that are effective against the bosses, his weapons deal lesser damage than X's and Zero's.