This fight seems to be a bit random, or at least that's how I felt.
First time I did it I was healing the tree and eventually ended up dying.
2nd time I was killing mobs and the tree died.
3rd time I killed mobs and healed the tree and it was easy as pie.

I can't really give any strategy as such, but just concentrate on killing the mobs asap and when there is downtime, use it as well as possible to heal the tree.