Although the bits do not fire their lazers at the same time, after the LAST bit has fired it's lazer, there will be about a 3-4 second window that you can cast your heals, that timing is what you should strive for.
The following strat is one that I came up with and it works extremely well for me whenever I run this. If you aren't in a static, you need to let your party know a few things.
1. If you are with another whm, figure out who is healing the main tank, and who is healing the rest of the party during the bomb and lazer phases. I personally ask the other healer to heal the tank while I heal the party since I am comfortable with the strategy I have. If you are with a sch, definately make the sch heal the MT, while you as whm heal the party during those phases.
2. Mark yourself with a sign. Tell the party to follow you during the bomb phases, and tell everyone to align themselves so that when Ultima uses aetherial boom, they get pushed to the south. Also tell them to activate the bomb you are close to when they see you start casting cure III, that way cure III will hit the party immediately after the bomb bursts. One cure III will heal the group to full hp. Detonate the North-South bombs first, then the East-West ones after. Let the off tank know either to go with the group, or stay away from the explosions, the OT doesn't need to explode one by themself.
3. As whm, cast protect on anyone that is raised, as we have shell with it aswell. If the other healer is a sch, let them know to cover the tank so that you have time to cast protect during battle.
4. Make sure to use focus target on Ultima so you can see when it does aetherial boom to position yourself to get knocked back to the south end, aswell as tank purge so you can precast your med/med II.
The reason I mentioned the above strategy, is that it makes the fight easier, aswell as the transition to the 2nd lazer phase easier. Since you are topping everyone up with cure III during bomb phase, there's no chance of someone solo'ing a bomb and dying, also saves someone from dying afterwards from either the green balls/ green line lazer, or tank purge right before the 2nd lazer phase.
After the bombs and green balls, Ultima will tank purge and it goes to lazer phase, make sure to precast medica II, and throw in a medica right after. If everyone is able to avoid the lazers, they should be full or near full health for the arms that come down on the sides. If someone does get hit, you can cast a cure on them in the window I mentioned in my first sentence, and you can also regen while running. For when the arms come down on the sides, you can do either a medica II at that moment, or if everyone is bunched up on top of you in the middle, you can cast a cure III, you will have to precast this aoe though. After that, it's more dodging lazers while getting in cures and regens when needed until the dps kill all of the bits. Once you get the timing down on this phase, the rest is cake.
If you are dealing with a sub-par co-heal or a sub-par tank, there are a few things you can do during this phase to help. You can divine seal+regen on the main tank, use eye for an eye, and virus if needed. You can throw in some cures if really needed as the rest of the group should have medica II still active, but make sure the dps's hp are near topped up for when the arms come down. Save your benediction for this part just in case too and use it if tank gets 1k hp or less. I tend to save presence of mind for in case Ultima goes on countdown to enrage, I spam stone II with it. If you are designated on party healing, and you are weaving in and out of lazers while casting heals, and the tank still dies, then there is a problem with either the tank or the other healer. Make sure the tank saves cool downs for this phase since both healers need to be moving around alot, have them save hallowed ground for this specific phase. Make sure the other healer is aware there is a window between lazers shooting that they can get healing in, and if needed they can eat a lazer or more, depending on their hp. Make sure they are also saving their cooldowns for this phase, as it is the hardest phase to cure in since you are constantly running around.