Avoid the dog chained to the wall ahead on the right. The door at the far right end of the alley doesn't open. From the starting position, move forward and pick up the chocolate bar (1) (10% health) in the doorway. Follow Lara's instructions and climb onto the bin to the left of the doorway.
NOTE: There's an achievement/trophy for collecting all chocolates but not eating any of them: "Chocollection." So be sure to pick them up but try not to use them. The "Good Boys" achievement/trophy requires you to not kill or take damage from any dogs, so steer clear of this one.
Move to the right edge of the bin and jump straight up. She'll automatically grab the ledge above. Press Forward to pull up. (You may notice a yellow grab bar appears below Lara's red health bar, at the top left corner of the screen, when she's hanging. More on this shortly.)
Once Lara is standing on the ledge, press Walk to activate walk mode so she doesn't accidentally fall off. You can hold Walk while maneuvering on ledges, but you can also press then re-press the Walk button to toggle Walk on and off. The blue Lara silhouette in the bottom right corner of the screen indicates Walk is activated. Walk to the edge and jump forward across the gap, as instructed.
Deactivate walk mode (by pressing Walk again), turn right, back up from the edge if necessary, then take a running jump over the railing into the alcove with the large health pack (2) (100% health) on the opposite side of the alley. The doors here don't open, so you'll have to jump back over to where you started.
Either take a running jump and press Action grab the railing of the opposite ledge, then press Forward to pull up, or jump down to the ground, then use the bin to climb up again.
Continue along the ledge toward the illuminated green sign. Lara wonders if she should go on or climb the ladder. In the original game, the area beyond the green sign was inaccessible without cheating, so you'd have to take the ladder. In the remaster, you can choose your path. We'll attempt to explore the whole area with all pickups and only a bit of backtracking.
For now, climb the ladder per Lara's instructions to reach the walkway above on the left. At the top, activate walk mode again to keep from accidentally vaulting over the low railings. Follow the walkway to the left and climb through the window as Lara instructs.
You can't open the padlocked wardrobe yet...
...but you'll find 160 euros and a chocolate bar (3) in the cabinets...
...and some Antique Doubloons (4) lying on the floor.
NOTES: Cash is counted separately from regular pick-ups. If you open your INVENTORY (Esc on keyboard, View/Create/Share on controller), cash is tallied at the top left. Other collectibles are stored under Health, Items, etc., and tracked under Statistics, near the bottom of the menu ring. (screenshots) A bit later in the game, you'll be able to sell items like these Antique Doubloons for cash. You won't need much cash to progress, but there's an achievement/trophy called "Cash Overload" for earning more than 3500 euros. To use items from inventory, press Up/Down to rotate the menu to the desired category (e.g., Health, etc.) Then follow the on-screen prompts to examine/use. Or, if you're playing on PC, check the list of keyboard Hotkeys under Options > Control > Shortcuts. At this point, you'll only have a few collectibles under Health and Items, but you'll soon acquire more.
Climb back out the window. Climb onto the white HVAC unit mounted on the wall next to the window opening. Face right and jump straight up to grab the edge of the opening overhead. Then press Forward to pull up onto the balcony.
Pick up more Antique Doubloons (5) just ahead.
Then follow the tutorial and walk to the edge. Jump forward across the wide gap and press Action to grab the ledge on the other side. Pull up. (The controls here are a bit different than in the previous games. Release Action once Lara has grabbed. Wait a moment and then press Forward to climb up. If you press Action again while hanging, Lara will let go and fall.)
Turn left, approach the low railing, stop, then press Forward to vault over the rail. (Yes, these controls are wonky, but you'll get used to them.) Pick up another chocolate bar (6).
Vault back over the railing and follow the ledge forward to the corner. Lara says she can hop across. Turn right and use the short hop maneuver (Walk + Jump) to cross the gap as Lara instructs. Continue forward across the small bridge made of planks.
Now climb the vertical drainpipe.
At the top, press Up + Right (or push diagonally on the stick if you're using a controller) to grab onto the ledge. Continue traversing to the right...
...until you can drop onto the shingled corner ledge. At the start of the game, Lara can only hang for about 15 seconds, so you need to keep moving or she'll fall when the yellow grab bar runs out.
Walk to the corner and jump up to grab the edge of the roof with the broken railing. Traverse around the corner to the right...
...and pull up onto the roof.
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