The following is the recommended order of Boss to take on based on weapon weaknesses. Note: Vile is weak against Yeti's ice weapon.

Bamboo Pandemonium
Earthrock Trilobite
Gigavolt Man O War
Avalanche Yeti
Burn Rooster
Optic Sunflower
Dark Mantis
Gravity Antonion

Use the following Boss order, with the corresponding weapon weakness.

Optic Sunflower (Green Spinner)
Dark Mantis (Shining Ray)
Avalanche Yeti (Shadow Runner)
Burn Rooster (Drift Diamond)
Gravity Antonion (Melt Creeper)
Earthrock Trilobyte (Squeeze Ball)
Gigabolt Man-O-War (Crystal Wall)
Bamboo Pandamonium (Thunder Dancer)
Vile (Drift Diamond)
Copy Sigma (Shadow Runner)
Sigma (X-Buster)
Lumine (X-Buster)
Lumine, Angel form (X-Buster)

Use the following Boss order. Each Boss' weakness is the weapon acquired from the Boss listed above it. Though Earthrock Trilobite's helmet is destroyed by the gravity weapon and it does more damage, attacking with guard breaking moves (full charge, third swing, eighth shot) will only knock the helmet off and he will be vulnerable while he tries to return to it.

Earthrock Trilobite (weak against Guard Breaks or Gravity Weapon; harder as he is not distracted)

Gigavolt Man-O-War (weak against Avalanche Yeti)
Burn Roster
Bamboo Pandamoniam
Optic Sunflower
Dark Mantis
Gravity Antionim