The start of this run is detailed in part 1, and the whole thing is shown in Treeble's quick video walkthrough.

About 3/4 of the way along the bridge, you'll come to a cluster of 5 gems, followed by a tricky section where you need to jump to the left to pick up a single gem...

...and then quickly run or jump back to the right to retrieve two more single gems in a row near the middle of the bridge. As soon as you get that third gem (shown at the top of this screenshot)...

...veer back to the middle-right side of the bridge to get the final red skull (5/5). It's hovering above a gap in the floor, so you'll have to jump through it to get it.

If you've found all 5 skulls, you'll receive a MAX AMMO UPGRADE. The last gem for the challenge is sitting just beyond the skull. Run over it and continue forward.

At the end of the bridge, large, white circles appear across the entire width of the floor, warning of an impending rockfall, so run/roll onto the safe ledge ahead as quickly as you can, but unless you're attempting the 10-minute challenge don't run through the exit yet.

During the run, if you fall through the floor and die, or if you reach the end of the bridge but missed some gems and/or the red skull, pause the game and choose reload checkpoint from menu. As long as you don't go through the exit, triggering the next checkpoint, you can retry the sequence as many times as you like.

If you managed to pick up all the gems on the bridge, you'll get a ring: the FROZEN BAND OF SET'S FAVOR (Torch Range+, Magic Shield Life+, Rate of Fire+, Weapon Damage+, Ice Armor).

The last 2 braziers (50-51/51) for the brazier challenge are just before the level exit. If you've managed to light all 51, you'll receive a MAX HEALTH UPGRADE.

[Part 1 | Return to the Tomb of Hoarfrost Walkthrough]