You'll meet up with the spirit of Carnan in Seregost, to follow the trail of Tar Goroth. Why the flame monster decided to hide in the winterlands is unknown, but then he did just wake up. Mount Carnan as you would a caragor to begin the hunt.
Goroth is easy to track- just follow the flaming footprints. Luckily he's not flying.
Ignore any orcs en route, and follow the trail to its inevitable ambush. In this next sequence, you'll be fleeing from Tar through an icy cavern- shoot the hanging icicles to slow him down.
Don't worry too much about ammo, you'll run through some elf shot deposits as you go. Just keep firing until you clear the tunnel. There's a cutscene where Carnan is taken out, and you'll face the Balrog on your own.
Immediately flee, using SPACEBAR to dodge his whip if necessary. It shouldn't take more than a few seconds of sprinting dead away to trigger the next transition, which you sees you fighting Tar Goroth from the back of a drakeformed Carnan.
The best strategy for this fight is also the simplest- just get right up in Tar Goroth's face, then hold the right mouse button (the same button you use in aiming your bow) to hover in place.
Using your ice breath will fill up your Might meter in no time, which in turn allows you fire off Ice Blasts- doing so three times fulfills your bonus objective for the mission. When Tal is weakened, an L-SHIFT prompt appears over his head- activate it to knock him through the ice.
Despite this dunking, Tar still seems to think that waging the battle on a frozen lake is a good idea. Dunk him twice more, using the exact same tactics, to end the fight (but not the questline) for good.
Tal's re-imprisonment completes the mission.
Note that you can still visit Tal in his icy, and extremely shallow new prison.