There are 5 phases to this boss that repeats three times. I made up names for the phases.
PHASE 1 - "CIRCLES"
Jinx casts a ring that expands for the entire floor 3-4 times. Jump to avoid.
PHASE 2 - "EYE LASER"
The floor tiles raises to different levels and the boss shoots lasers out of his eyes. Double jump around to avoid.
PHASE 3 - "FIRE STORM"
Two walls raises at the left and right hand sides and shoots fireballs in preset patterns. It is however random which pattern you get. Look for larger clear areas and jump / double jump to them.
On top of the fire the floor will move during this phase but if you focus on avoiding the fire it's easy enough to jump to places where there are tiles. Try to stay in the center of the platform as much as possible.
During the third round it helped me to turn the camera to another angle to easier see the clear spots but the change of perspective might make it harder. That's up to you.
PHASE 4 - "LABYRINTH"
Walls will be raised and a red orb spawns on one of the tiles. The orb will explode if you don't hit it in time costing you one heart. On the other hand if you hit the orb it will be launched towards Jinx and hurt him.
Should you fail to hit the orb and if you don't die you will go back to the previous phase for another round of fire.
Position yourself on the "dot" between the intersection of four squares. See where I position myself in the video - you will pushed on top of the walls if you do it right and it will be faster to jump to where the orbs spawn (as opposed to actually running through the labyrinth).
Hit Jinx with three red orbs to defeat him.
PHASE 5 - "CRITTERS"
Two bees and a maggot or a fire golem will spawn. Each one of these gives you one full heart as you kill them so if you get hit during any other phases this is your chance to heal.