You, as Sly, will first have to jump onto the laser beams while Dr. M is aiming fireballs at you. You will then jump to grab onto Dr. M's hooks. Once you have successfully hooked, he will be drawn to the center of the stage, where he will then latch himself to the ceiling to shoot a laser at you. To avoid the laser, hide under the vehicle that will appear, allowing the laser to destroy the vehicle and causing Dr. M to come down to the arena. Hit him as you would normally fight an enemy once he is on the ground, while dodging his attacks (mainly water attack). After you have dealt enough damage he will return to the air.
You will repeat what you have done in Phase 1. Be careful that Dr. M's attacks this time are electric-based, such as his slow-moving homing balls or his dash towards you. Timing your counterattacks is key.
You will repeat what you have done Phases 1 and 2. Be careful that Dr. M's attacks this time are fire-based, and he will create multiple slow-moving fireballs if given the chance. His dashes, likewise, leave a fire trail behind him that can deal damage if you're not careful. As with phases 1 and 2, timing your attacks are key.
Control will switch over to Carmelita, where you will need to shoot Dr. M about 5 to 6 times to completely deplete his health.