Phase 3
For the most part phase 3 is identical to phase 2, it only changes when the nail part comes around. This time you will have 13 nails to deal with and one of them is a large one in the middle. Reach the nail phase the same way as you did in phase 2 while holding your damage buffs for the nails.
How you handle the large nail is dependent on your group setup. If your group has a melee damage dealer you will take out the large nail first by use of the melee LB. This will take around 80% of its HP off so the group still needs to apply some damage it. However if your group is all ranged DPS then you will take out the big nail last with the caster LB. This is because the caster LB will kill multiple nails if used early and the added AoEs from nail destruction will wipe the group.
Whichever way you do this you should kill the smaller nails in a clockwise direction just like the last two phases. BLMs in the group can actually hit two nails at once with Flare, but in general single target damage is better.
Once all nails have been destroyed or you fail to kill them all in time Ifrit will perform another Hellfire.
Phase 4
Phase 4 is the same as phase 3 for the most part, except there are no nails. If you reach the point where nails would have appeared it is game over. Ifrit will not spawn any more nails, he will simply jump for Hellfire and wipe the party. This means you ran out of time. As a result phase 4 itself is a DPS check, though if everyone is alive you will have no problems finishing him off in time.
Ifrit phases