Like so many other things that are reinvented, Onyxia seems to divide the World of Warcraft demography. As always, the most vocal side are the ones not happy with Onyxia's reincarnation, finding a long list of faults in her new forms but personally I am delighted from the update.
The very first reason to like her is the fact that a huge portion of us never got to fight her in vanilla WoW and have only seen her, mainly lying on her back after being zerged by a bunch of level 80s. I, myself took her down with just the three of us, and even from our tiny group two of us were tanks. To make it further ridiculous, the paladin tank also functioned as our healer, who is the same paladin who I know 1-manned her.
This is the case with all old raids and for my life cannot see what the point would be to not redesign them, so they can provide a logical function in the game - instead of just being the occasional punching bag for nostalgic old timers.
The second reason is that now Onyxia is a lot more approachable, instead of feeling like teeth being pulled. Naturally, for some this is a bad thing. Of course, I bet it was a blast to spend over 40 minutes fighting one raid boss. With luck, someone screwed you over because of their teenage angst and you would be starting all over again.
Third but not last, with Naxxramas, Sartharion, and Malygos becoming obsolete we desperately needed a new raid into the game. Granted, it is only one boss but it is better than nothing while we wait for the release of Icecrown. Of course, I do not mean that in condescending, but rather pointing out the fact that those of us who have completed Ulduar, Trial of the Crusader only provides so much entertainment.
So what is Onyxia like these days. After research (and listening to old timers whining), I do not see how the fight is so much different; you go through three distinct phases and a lot of moving around is required to get through them.
Phase 1 is a simple spank phase. Your main tank should tank her against the back of the cave, so the push back does not blow him away and everyone else should stay around or behind Onyxia, to avoid the frontal cleave that can easily turn a clothie into some shredded wallpaper.
Phase 2 begins when she walks back across the cave and takes off into the air. As in the vanilla version, everyone should group up in the middle of the cave, where the floor declines into. Whelps will fly from both sides and your (preferably an aoe capable) tank grabs them while dps aoes them down.
There is an elite type of add that also comes from the entrance, which must be tanked and killed as quick as possible, for they hit rather hard and will overwhelm the tanks if not taken care of. Most notably have your cloth wearers dispel the Ignite Weapon as quickly as possible, for it adds 25k extra damage to their attacks for five seconds.
This phase ends when the ranged dps succeed in bringing Onyxia to 40%, after which your main tank must quickly grab aggro and place himself against a wall, or she makes wind chimes of your raid.
From there the fight continues much like phase 1, except for an occasional inconsequential whelp, fear, and fire cracking from the floor. If you get her this far, you should be able to nail her, as long as you healers do not run out of mana.
All and all, a very enjoyable raid in my opinion.