Stand in the middle of the doorway. Walk to the edge and then walk one step back. Then do the following series of jumps to land on the tiles: standing jump forward, side flip to the left, jump forward, jump forward, side flip right, and jump forward to land in the alcove. If you fall through you can climb out easily, but you'll have to reload a saved game to try for the secret again.
If the jumps are too tricky, try this alternate method: Stand in the middle of the doorway, walk to the edge and hop back once.
Take a standing (not running) jump forward to grab the edge of the first break-away tile. As long as Lara hangs there, the tile won't start to collapse.
Pull up. . .
. . . and immediately take a running jump to grab the edge of the tile straight ahead near the alcove. Pull up and run into the alcove before the tile breaks. (Thanks to Mark R. for this alternate strategy.)