Instructions
Collect the ammunition for Bart's slingshot in the room with the UFO. Search the room thoroughly to ensure that you have collected all of the ammunition. That way you will not run out of ammunition in the middle of the boss fight when you need it most.
Defeat the guards in the room so that they don't interfere during the boss fight. Use your standard melee attack if you can so as to preserve ammunition.
Climb the scalable rock wall as Bart.
Use Bart's double jump and glide to reach the center UFO. Timing is important: You can get on the UFO only when it is low in its up-and-down pattern. Getting there will scare Jimbo and cause him to go to the ground, setting up the boss fight.
Press the L1 button to create a target lock on Jimbo and press the Circle button repeatedly to fire your slingshot at him.
Move constantly during the fight and maintain as much distance as possible to give yourself maximum reaction time to avoid Jimbo's laser blast, which is a powerful attack.