The sequence below is also shown in this short video.

In the last section, we climbed up through the abandoned building to reach this ledge, overlooking a large, rectangular room. The remains of the decaying roof are similar to the collapsing tiles you've encountered before. To unlock the achievement/trophy "With Respect for Cultural Heritage," you'll need to "cross the broken roof by dropping only three wooden panels."

You may be able to find a different path, but I'll share what worked consistently for me. The tiles outlined above are the only three we'll touch as we cross the room.

Begin on the left side of the starting ledge. Walk to the edge and hop back once, as shown above. Save the game, since this may take a few attempts.

Take a running jump to clear the first row of wooden slats...

...and land on the middle tile in the second row. Briefly release all buttons as Lara lands. Then quickly take a standing jump across the gap onto the next tile (i.e., the right tile in the fourth row).

As soon as you regain control, take a running jump, steering slightly to the right, to clear the gap and the next row of tiles, then land on the single tile beyond.

Without hesitating,
take another running jump, again veering slightly to the right and taking off before Lara touches the last tile. If your timing and angle are good, she'll land on the wooden ledge just beyond the sloping roof...

...and the achievement/trophy will pop.
NOTE: If you don't care about achievements/trophies, there's an easier route in the archived classic guide.
DARK MODE: I plan to add optional dark mode for these pages, but my current priority is updating the walkthroughs. Meanwhile, may I suggest a reputable dark mode browser extension, such as Dark Reader? (Download only from trusted sites, like darkreader.org or your browser's official add-on/extension site.)
Walkthrough text and diagrams copyright © Stellalune (email ). Feel free to copy or print this walkthrough for personal use. By all means, share it with friends, but please include this credit line so people can send me their feedback. No part of this walkthrough may be reproduced on another site without permission.