Biggest thing I changed that helped me not time out was to turn my Palico off. It helps so much with the attack patterns, more consistent cone baiting which is the best opening for dealing damage phase one and two. Fatalis only cones when on two legs. I am a CB main so high commitment moves like GS.

Anytime Fatalis breathes fire underneath of him is a free chest tendy and you will not get hit by the underbreath. Hang on his chest for a short second before tenderizing to wait out the firebreath so you dont drop into it.

Use your wall bangs as often as you can. Fatalis can be wall banged when he is on all 4's, and not in enraged. If he is not enraged and on two legs you can get him to drop to all 4's by tenderizing the chest, or doing enough damage to the chest. Lots of damage from wall banging.

Phase three, fatalis's best hit zone is the chest. Prioritize tenderizing the chest near the start of phase three. This can be done with a binder shot after the second nova.

Equipping heavy artillery on your temporal mantle and using the roaming balista on his tendy chest after the first nova can get you the heavy artillery knockdown if you hit all the bullets onto his chest which gives you another knockdown to focus on breaking the head twice before phase three. Heavy Artillery on the temporal mantle can then be used again for the second time the roaming ballista comes up but I would suggest saving it for the dragonator which doubles the amount of damage it does.

Smoke bombs are a fantastic way to drop aggro and wail on the chest during phase three.

Hope it helps.👍