For first phase (while your group is killing first leg) keep an eye on the OT too, he will be eating orbs, dealing quite a bit of dmg to him. Make sure one of the tanks stuns the leg, when it is giving off steam. It's a party-wide aoe that can get annoying to constantly heal through and can easily be avoided.

During Doll phase try to avoid aoe-healing too much, as you will be pulling hate from the dolls. They put stacks on you, if you get 3 you will blow up and probably die. Dps should grab those and keep them away from you, still they are dps and can't hold hate against massive aoe heals so well, so try to make it easier on them by not doing that

Last phase (after second leg is down and group is dpsing the body) a debuff will be placed on both healers. Handling this is crucial to surviving the fight. Heal yourself up as necessary and avoid getting too close to the other group members, as the debuff will be passed on to others on touch. Specifically watch out for this when dodging aoe. After the debuff falls off, you will have a few seconds before it is reapplied to you. I usually use this time to go into the middle and pop an aoe heal for the group (medica2 usually since I'm playing WHM but I'm sure the AST has something similar).