Lara Croft and the Temple of Osiris

I've created a two-part 100% walkthrough video. It covers every single achievement in the game except the co-op ones and the speedruns, but the co-op are self-explanatory and the speedruns are super easy once you've played a level, since you can usually just run past everything and solve the puzzles most of the time. Contrary to some reports, you CAN get the gold points challenge on EVERY tomb on your first time through in solo play, even this one. Follow along with the video below as you play through the game (and part 2) to have your 1k in 8-10 hours tops. A detailed text guide follows after the time stamps for those that prefer it, copied over from the walkthrough I've written for this game.

This achievement will require you to return to the Pyramid of Osiris for the speedrun during the post-game. All of the other tombs can be completed (including the speedrun) during the main game, but this one is locked out after the first run until you defeat the final boss. You'll get everything but the speedrun the first time if following my guide.
A helpful tip on finding this level to replay it from MaxLive360 below: "I assumed "Pyramid of Osiris" meant the boss fights, but it's actually the first level I think. After finishing the game you need to go back into the pyramid and press B on the red pylon to open the door and play the actual "Pyramid of Osiris" level."


Timestamps:
00:07 - Pyramid of Osiris
13:32 - Tomb of the Timekeeper
22:08 - Challenge Tomb #1
25:00 - Tomb of the Silversmith
35:42 - Challenge Tomb #2 (west/southwest from Tomb of the Silversmith)
37:55 - Khepri's Tomb
42:52 - Oracle of Osiris
46:50 - Challenge Tomb #3
49:50 - Tomb of the Ferryman
1:02:22 - Challenge Tomb #4

Challenges: Bronze/Silver/Gold – 100,000pts; Complete in under 6:00; Collect 5 Red Skulls; Free a Skeleton from its sarcophagus; Knock 3 Skeletons onto spikes with your Remote Bombs; Destroy all of the tomb’s Arrow Traps

When you pick up your first weapon during the course of this tomb, you’ll unlock Gotta start somewhere. Also, keep an eye out for the small floating jars from where other players have died and grab at least five of them to unlock your first onyx weapon as well as the Your death won’t be in vain achievement. Break EVERY sarcophagus you see. Some of them have skeletons inside (randomized) for extra points as well as freeing a skeleton from a sarcophagus. Also destroy ALL of the arrow traps as you go through. There are a total of 35 to destroy, and if you don't have 20 destroyed by the time you reach the final escape sequence that means you missed one somewhere along the way, as there are 15 during the escape.

From the start, follow the path forward and light two braziers at the base of a ledge to raise pillars that you can climb up to continue. You’ll reach a large room with spikes blocking the exit and a golden rotating ball in the middle that shoots fireballs at you. Shoot it with the light from your staff and follow it around clockwise to shoot it a total of four times and open the way forward. You’ll reach a short cut scene introducing you to skeleton enemies. Before going up the blue platform on the right, destroy the orb on the left with your staff’s light to open the door below the ledge and reach Red Skull #1/5.

Continue up the path and grapple up, then use the blue platform to go up again. Deal with the scarabs that come out, and use the grapple point to your left to carefully lower yourself down to Red Skull #2/5 over the ledge. You’ll go right up a narrow path with arrows shooting across from off-screen. You can’t destroy their sources, but ahead of you is a set of arrow traps blocking the way forward. Make sure all of them are destroyed with your bombs before moving on.

Just beyond that sarcophagus is a square area with a spike pit past it and a grappling point high on the left. There will be several skeletons in this area, so use your bombs to knock them off the ledge into the spikes. If you’re doing this late in the game, you may need to equip a ring/amulet that decreases your bomb damage rather than whatever you’re currently using. Knocking three skeletons into the spikes will complete the challenge. Once you climb the ledge with the grappling point, you’ll reach another glowing orb just ahead. Bomb the three arrow traps on the right and destroy the orb with your staff. You’ll go through that door and down three sets of stairs, and see arrow traps to the right. Jump over and blow the three traps up, then go to the far left and destroy those three.

Continue along the path and a bunch of skeletons will arrive. This is another opportunity to use your bombs to knock them onto spikes. After dealing with them, destroy the three arrow traps by the blue platform and ride it up to Red Skull #3/5. Continue to the right past the spike door and blow up the three arrow traps by the pressure plate, using the plate to lower the spikes blocking the way forward. Watch the cut scene, and shortly ahead you’ll reach a room with stairs down to the left and right. Go left first and use the round blue platform with your staff to jump over to the spinning round spike pillar below the high ledge. From it, jump up to the ledge and push the honeycomb ball down over the side closest to the spike pillars. Roll it over near the one with Red Skull #4/5 on it, and jump onto the ball and up to the pillar to get the skull.

Now roll the ball up into the upper-center platform and into one of the two receptacles. Go down to the right and bring that ball back, placing it in the other receptacle. A bridge will extend, giving you access to a submachine gun and the way forward. This is your first weapon pickup, so you’ll unlock Gotta start somewhere.

Drop down and continue to the right and use the grappling point to climb up after dealing with the skeletons. Go up the first blue platform, but before going up the 2nd, jump back above the grappling point you just used to get Red Skull #5/5. Ride the 2nd blue platform up and continue on to initiate a short scene followed by a chase escape. At the end of the escape, exit the dungeon and you’ll unlock A journey begins. Assuming you got the 5 red skulls you’ll unlock Gotta have them all, and if you managed to keep your multiplier at x4 and get the gold score challenge done, you’ll unlock Learn from the best.