The Exploiter Orb fight can be started at Deck 12, the entrance to which is in a cave, as seen here. Once inside, deposit your Diluted Thermia here (only the squad member depositing it loses theirs). You can obtain Diluted Thermia from Thermia Fractures, which has its own separate guide. (s/howto thermia fractures)
Phase 1) The Exploiter Orb will spawn from the opening at the top of Deck 12. After shooting out the rocks she’s standing on, go behind her and shoot out one of her 4 vents. The rest will freeze up with ice and become invulnerable to further damage, and she will then move to the other side of Deck 12. Thermia cans will soon start spawning at 4 nearby locations (look for canisters on the ground in the area), and you will need to throw them at her vents (by pressing alt fire as prompted) to thaw them out in order to destroy them. Shoot the cans in mid air to detonate them prematurely to make it easier to cover the vents. With just one vent left, the Orb will once again move, this time to the ceiling of Deck 12. Either parkour up there to hit her vent or wait for her to come back down. The small green “Mite” Raknoids will spawn throughout Phase 1, so this can also double as a decent Vega Toroid farm. After all 4 vents are destroyed, Phase 2 will initiate, requiring you to return to the surface.
Phase 2) Once outside, the goal is to make the Orb overheat. Keep an eye out for coolant Raknoids that will spawn and walk up to Exploiter, shooting coolant at her to cool her off. This will reduce the heat gauge, and killing the Raknoid afterwards will not spawn a coolant cell, so kill them off quickly. Exploiter will slam the ground and spawn Thermia Fractures once the heat gauge fills a little; carry the coolant cells dropped by coolant Raknoids to these fractures to create Thermia cans which can then be thrown at the Orb to speed up her overheating. Once the gauge is full, bullet jump close to her to trigger a cutscene that will have you rip off parts of her body. Shoot the exposed parts and repeat this twice until she dies. Loot will spawn behind her, and after a short while she will explode.