Tomb of Hoarfrost - Pool with Frozen Islands

Lara Croft and the Temple of Osiris screenshot
As you enter this area, the gate closes behind you. Then, when you hop over to the nearest ice island...

Lara Croft and the Temple of Osiris screenshot
...3 Marks of Set appear and begin to disgorge enemies. Keep moving but try not to run through the Marks or fall into the pool as you fight. The cold water won't hurt you, but you may end up taking damage while swimming around looking for place to climb out. In the single-player game, it's probably best to stick to the higher, C-shaped part of the larger mass of ice and just keep moving back and forth. This strategy is detailed below.

The gate to the northeast does not open until you've defeated the last enemy, so even if you're attempting the 10-minute time challenge, you'll have to fight them all. You can save a little time by using the Staff to close the Marks. If you're going for the score challenge, you'll want to fight all the enemies for points—and of course try to avoid taking damage in order to keep your score multiplier maxed.

Lara Croft and the Temple of Osiris screenshot
If you have not already beaten the Challenge: Kill an Enemy Using an Exploding Mummy's Self-Destruction Attack, this is another opportunity. Shoot or bomb one of the large mummies when it's standing near other enemies...

Lara Croft and the Temple of Osiris screenshot
...and you'll be rewarded with the FROZEN MARK OF SET'S ASCETIC (Cold Resistance, Defense+, Speed+, Ammo Efficiency+, 10% Cheaper Items).

Lara Croft and the Temple of Osiris screenshot
In addition to the enemies that emerge through the Marks, other foes pop up here and there, including a giant ice skeleton carrying a shield. To defeat the giant skeleton, you must either attack it from behind, bomb its shield away, or use armor-penetrating weapons. I prefer the railgun (unlocked by beating the gold point challenge in Tomb of the Torturer), since there's no risk of accidentally injuring yourself or your teammates, which sometimes happens with grenades/rockets. You can also move back and forth along the top curve of the island, leading enemies behind you.

Lara Croft and the Temple of Osiris screenshot
Drop remote bombs as you go...

Lara Croft and the Temple of Osiris screenshot
...and detonate them to kill or at least weaken pursuing enemies.

Lara Croft and the Temple of Osiris screenshot
Turn and fire as the survivors come toward you.

Lara Croft and the Temple of Osiris screenshot
Then run/roll past them and repeat the process. There's plenty of room here to maneuver, and you should be fast enough to stay ahead of most enemies.

Lara Croft and the Temple of Osiris screenshot
Before too long your bombs should take care of the skeleton, or you can shoot it to finish it off.

Lara Croft and the Temple of Osiris screenshot
When you destroy the last enemy...

Lara Croft and the Temple of Osiris screenshot
...the exit opens, releasing a shower of gems. If you're not attempting the time challenge, take a few minutes to explore the room, gathering gems, health, and ammo.

Lara Croft and the Temple of Osiris screenshot
Swim down to the lower corner to find a red skull (3/5) sitting on a small island.

Lara Croft and the Temple of Osiris screenshot
When you have everything, head up the stairs to the northeast

Lara Croft and the Temple of Osiris screenshot
Be sure to light the brazier (28/51) on the right side of the staircase for the brazier challenge.

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