Phase 1 - The Mini-Minions
In the first phase of the battle, the boss will release mini-versions of himself called "Nexos." While these minions are attempting to attack you, the boss will shoot fire blasts at you. His weakness in this phase is the fire blast shooter, which you'll need to destroy, along with all the Nexos.
Beating Phase 1
Use the PK and the Zap-O-Matic guns to kill the Nexos. While keeping these Nexos at bay, use your "Freeze Time" ability and shoot your ion cannon at his fire blaster until it has taken considerable damage, at which point the battle will automatically move to phase 2.
Phase 2 - The Lasers
With all the Nexos killed and his fire blaster damaged, the fire blaster will begin shooting powerful lasers. He will no longer release Nexos during this phase.
Beating Phase 2
Avoid the laser blasts as best you can while using your jet pack to get to a location above the beast. As you get above him, shoot your Zapo-Meter at his fire/laser blaster until his health depletes.