Trial of the Crusader (10 man) can be soloed by hunters, without much effort.
Spec: Beastmaster. Pet: Corehound, for heroism. Make sure to have Heart of the Phoenix available.
Gear: Half 5.2 PVE Raid Finder and half epic PVP gear.
Northrend Beasts
There are three mini-bosses. Save all your burst including Heroism for the second mini-boss (the two giant snakes).
You will get a debuff that will paralyze you and you will die if you don’t kill the two snakes before the timer goes off.
The third mini-boss, just nuke him.
Lord Jaraxxus
Nuke. Nothing special.
Faction Champions
Kill the healer first and the casters while kiting the melee mobs.
Twin Val’kyr: Fjola & Eydis
Just nuke one and try to avoid the beams. They share the same HP.
Anub’arak
Nuke. Nothing special.
You can solo this raid for fun but don’t expect to get any fancy gear for transmogrification, at least for Alliance. I know that there are different gear models for both Alliance and Horde.