Onyxia strategies...

[Lissa]

The main problem in that transition is healing aggro.  If a healer heals somebody near Onyxia before the main tank builds up any aggro (note: it doesn't have to be the main tank who was healed -- just someone who happened to be near Onyxia when she landed), Onyxia will charge right to that healer and smack everyone in that area around.  This is particularly a problem for Horde players who don't have the benefit of placing Fear Ward on their main tanks.  If the main tank gets feared in the middle of the room, they can run far enough away that their aggro wipes, and Onyxia will charge the healers.

As far as solutions go, there aren't many easy answers. For alliance, it seems that it would be a bit easier -- make sure the main tank has Fear Ward on him or her, make sure the main tank is waiting there for Onyxia when she lands, and make sure people aren't nuking her when she lands.  For Horde, it's a little trickier and messier, but basically, the main tank has to do whatever he or she can to make sure they don't get feared away while backing Onyxia up to the north wall.  Again, all dps should be off until the main tank establishes aggro (tell people to focus on killing the remaining whelps if any).  Also, make sure that people aren't anywhere near the whelp caves when Phase 3 is near.  Otherwise, it's pretty much set up a good system of out of combat rezing to rez anybody who does get killed in that phase transition.  Once Onyxia is up against the north wall and once enough healers are up to heal the main tank, Phase 3 is easy.  It's just the transition that's hard.
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With the changes in 1.7, Fear Ward will likely not be needed as much. With Warrior skills/buffs sticking with changing stances, Warriors will mostly be stance dancing to keep the fear off now. Both sides should have a pretty equal chance in 1.7 due to this change to warriors.