Have you ever played Ikaruga? It's a pretty intense, if somewhat old, game, and this fight is based off the same mechanics. It is pretty simple in execution, and extremely light in healing so long as everyone does their job.
To begin with, split the raid in half (as well as you can for having 25 people) and start opposite the large entry doors. Those tanking/attacking/healing the white Val'kyr (Fjola Lightbane) should have dark auras, and those tanking/attacking/healing the black Val'kyr (Eydis Darkbane) should have light auras. At the beginning, like most fights, the only one who should need healing is the tank you are assigned to (though there are no penalties for scooting near the middle and being able to hit both tanks). Make sure each tank has their focus in between the portals of the right or left side.
The only time the fight becomes healing intensive is during the "bullet hell time" and that is only if you and your raid members are not careful to avoid balls of light/dark, as you only absorb those of your own type and those of the wrong type cause damage. As a healer, you should avoid all balls as they are much more beneficial to the DPS than you, and they will need them for the shield portion of the fight.
Otherwise, your only other job is to watch for Vortexes and change your color if it is appropriate. Blizzard has generously provided a warning for you, all you have to do is read it. If you are "dark" and light is being channeled, you need to click a light portal, and vice-versa. There is no healing through this. If someone is wrong, they are dead.
Since you're a healer, you don't have to worry about shields other than to know that once a shield is up, the DPS needs to burn it down so they can interrupt the heal. If you have the spare time and can pop up some damage on it, it wouldn't hurt. As was mentioned before, this fight is very undemanding of healers so long as everyone avoids the wrong color orbs.
My guild downed the Twins first try with six healers (25 man), and we're considering doing it next week with only three. For most of the fight, our healers had very little to do. So, this will really depend on a few things: how much DPS you can output to burn shields, how reliable everyone is in avoiding balls of the wrong color, and how aware everyone is in switching auras. If you can coordinate healer population with this information, then the fight should be a snap.