The official description for this achievement/trophy is, "In your nightmare perform double somersault to get to the trapdoor at the foot of the sculpture in order to obtain the Uzis." Details follow.
IMPORTANT: Do not try hanging from the edge before you jump or dive. The trapdoor is triggered by Lara moving through the square directly in front of the spot from which you dive, and it only cycles once. So if Lara hangs from the edge and then pulls up, the trap door will open and close. Then, when you attempt to dive, the door will remain closed, and Lara will crash and die. If you do this by mistake, and don't have a convenient save, you'll have to restart the level if you want the achievement/trophy.

After gathering a few pickups in the ZOO with the big bird boss cage, as shown in the last section, return to the ATRIUM WITH THE HUGE SCULPTURE. Now look waaaaayyy down. There's a small, square trapdoor at the base of the sculpture. That's where you're headed.

Save the game because you'll need to do more gymnastics for the "1980 Summer Olympics" achievement/trophy. Walk to the edge. Walk one step back.

Hold Walk, then press Forward + Jump to do a swan dive.

As soon as Lara is airborne, hold Roll to do two somersaults on the way down. The trapdoor opens as you fall, and the room below is flooded, so Lara should splash down safely...

...and the achievement/trophy should unlock.
(Or, if you don't care about achievements, just take a standing jump from the edge of the walkway into the trapdoor.)

The trapdoor closes, sealing you inside the flooded room, but there's a small air pocket just below the trapdoor. Scattered around the floor are the UZIS and 4 sets of clips (24-28). When you have everything, swim along the narrow tiled passageway...

...and through the door with the 'K' on it, which opens as you approach. You'll emerge in a SWIMMING POOL. Get air if necessary. Then retrieve a second HOTEL KEY (29) from the bottom of the pool.

When you return to the surface, a gangster (4) is taking potshots at Lara from the shallow end. Quickly climb out of the water and kill him.

You're now on the LOWER LEVEL of the ATRIUM. The double doors near the swimming pool won't open until you replace the missing CIRCUIT.

For now, move out into the ATRIUM. Head for the area to the right of the sculpture. Roll...

...and take out the 2 armed bad guys (5-6) who appear near the SWIMMING POOL.

Relieve them of a small medi pack and 2 boxes of shotgun shells (30-32).

Then return to the alcove decorated with tropical foliage near the sculpture. Use the HOTEL KEY in the lock to open the doors.
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