Inspect the cage with the skeleton in it for [JOURNAL ENTRY #3]. Go down the trail to the right and you'll reach a bridge. Before crossing it, check out the left lower side of the path to find a small passage towards treasure #27 [LANTERN MOUNTED FLINTLOCK].
Cross the bridge and head up the right side of the path, then slide down the gravel slope. Climb the ledges and head upstairs, then make your way to the end of the path. You'll now be in a puzzle room. Grab the bucket from the middle of the device and head into the water on the left side of the area, then hand it to Sam.
You can now operate the four circles on the device. It's not hard to figure out what to do: the small white cross needs to be placed in the lower left light, the big cross needs to be placed in the middle, and the small black cross needs to be placed in the lower right light. In order to solve the puzzle you must first separate the crosses from the other circles. In concrete terms, this means the big cross needs to be placed at the very top spot, the small white cross needs to be placed at the far left spot, and the small black cross needs to be placed at the far right spot. You can then align the small white and black crosses, followed by the large cross. The bucket should then be at the top spot.
Press the button next to the door to open it. Before you continue, check the button again to get [JOURNAL ENTRY #8]. Now head through the doorway and go to the far left side of the path. Sam will remark something and you get the possibility to have [OPTIONAL CONVERSATION #8]. Turn back and head left, following the path curving to the right, but before going that direction, check out the wooden pole sticking out of a rocky wall down below, barely visible. Climb down the ledge here tp swing your rope towards it. You can now, with a little practice, swing to the platform on the other side, where you can find treasure #28 [STRANGE PENDANT]. The Last of Us players will instantly recognize the Firefly logo on the back of the pendant.
Head back to the main trail and follow the steps and leap over the gap, then use the rope to swing to the path down below. Here, facing the ravine, move to the edge on the right of the pillar and climb down to find treasure #29 [AMATORY BOX]. Head back up afterwards.
In this area, climb up and boost Sam to the broken ladder. He'll push down a cart for you that you can place near the 'pillar'-like ledges, allowing you to reach them. As always, these are recognizable by the little snowy spots on them. Head up and crawl through the tunnel, then go through the two crypt chambers and climb up to the next area. Jump to the ledges near the wooden beam and crawl up to trigger a scene. Continue to the right, then drop down.
In this room, go to the far left corner and move behind the fallen statue in the adjacent small room to find treasure #30 [PEWTER BOX]. Move to the other side of the crypt and use the rope, but instead of swinging over the gap (something I'm sure you wanted to do initially), climb down the rope and swing to the left, underneath the wall, onto the platform behind it. You can then climb the nearby wall and push the cart at the end of the tunnel to move on.
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Align the cart, climb up and go through the arch/doorway, then look to your right. You've reached the destroyed bridge, but now you're on the side where you want to be. Climb down the ledge to the right of the destroyed bridge to find treasure #31 [MEMENTO MORI SKULL WATCH]. Continue down the main path, through another arch doorway and cross the bridge, then use the rope on the heavy cart on the right upper side. Climb up and check the right corner (among the stuff) to find treasure #32 [SCOTTISH TIPSTAFF].
Now push the heavy box down, and continue pushing it until it's in the corner, near the edge of the ravine. Attach your rope to it and swing forward to the ledges, then follow the straight path. Go through a small tunnel and you'll reach another open area. Drop down to the platform below and inspect the corpse for [NOTE #2].
Move over the wooden beam, jump to the next platform and carefully try to cross over the seesaw. Sam will call you back, since the thing moves down. He'll jump at the other end, allowing you to grab the ledges when at the upper end. Use the rope to swing to the right side, to a mechanical wheel, and reach the upper platform this way. Here you can find a heavy cart - how convenient - which you should drop on the seesaw. Cross it and make your way to the end of the linear path afterwards.
After the scene, jump over to Sam, then climb the two towers and jump to the path. Beat down the Shoreliner and grab his gun. Exit the cave while shooting any Shoreliners in your way. When you reach an open snowy area, defeat most Shoreliners first before running up towards the guy behind the turret in the middle of the area. In the next area, use the rope to reach the other side, then use the rope on the crane. Again, defeat all Shoreliners around here. Head down the path and defeat more Shoreliners. When you come across the Mettler M-30, lying on the left side of the path on a box, take it along. It's a little better than the other machine guns. In any case, continue descending the linear path from here.