If possible, before getting close enough to engage Blackheart, find the structures that look a little line phone booths made out of stalagmites. Destroy each of the 6 structures first. Any remaining ones will act as respawn points for Blackheart when you kill him. Without them, he will just die. The structures will emit an energy blast that pushes you away if you try melee, so using ranged attacks is quicker and more efficient.