I gave it one real attempt, got tripped up in P2 due to the whelps and dragon guard, I probably could've managed it if I put more time into it so I'd say yes, hard part is maintaining your health without getting hit by any melee attacks from adds, Onyxia's fire hurts in P2.
I two man it every week with a friend now, so I never really thought of trying again. (I was MM with iLevel389)
Hunter maybe, if you can get your pet to keep aggro on the adds. Ret pala, im not sure really having never played one. I managed to solo her on my DK, it was mind-numbingly slow, but I got it done. For melee it takes a very long time because you have to dps her down while shes in the air.