As some of the Challenge Mode "Gold" Achievements are now already accomplished, you can see a clear trend to class stacking or, better said, "must"-haves, while some classes (seemingly) can not compete.
There are two main tactics right now:
1) Blood Dk Tank + 4 Dps (hybrid healing with elemantal shaman, shadow priest or moonkin)
2) AoE/Burstclass/Cleave stacking (elemental shaman, demo lock, dk)
Elemental Shaman pulling 120k dps with 463er gear is ridiculous, Stormlash Totem adding up to 15% of total Dmg on a Boss pull is crazy. (part of that is that elemental shaman has 100% crit chance and crazy dps cooldowns, thus performing incredibly better then classes that depend more on gear to enable comfortable (and relyable) playstyles... for example fire mages are totally screwed and rng-dependant in low-gear because of low crit chances... taking a fire mage to a boss with bloodlust/trinket proccs and him not critting cuts his Dps from 90k (very lucky) to 25k (very unlucky), thus failing the whole instance for the group...)
Another Story is CC, crowd control is absolutely out of the picture, except for stuns. Sheep, Sap, Sleep etc... are totally useless because it only slows you down (you do not meet DPS requirements of you single-target nuke 1 trash mob after the next), unless you can entirely skip a trash pack with it. Some instances (GSS requires all trash mops to be killed except for one) are not do-able Dps-wise if you must rely on CC (thus 4 DPS 1 Blood Dk -tactic), while other CC is totally overpowered (Aoe Stun, AoE Silence, AoE Interrupt), allowing you to "tank and spank" up 3 elite packs (8-9 mobs) at once.
I know it seems a bit early to tell and judge, and I am sure there are some tricks for one or the other instance where a specific class might shine/used for bugging, but to get gold on every challenge mode (or at least the most), you'll be required to run the same few overpowered classes until blizzard nerfs them and buffs other comps.
But I guess balancing challenge modes will never happen, so maybe throw away your healer and reroll something else...