How many endings must I see in Deus Ex to earn the “Deus Ex Machina” achievement

I think I'm around half way through and I've found around 20.

A good rule of thumb is to always have a couple spare, so if you come across a five story drop that you have to survive or a level 5 security device or a wall you want to punch through, you can without having to look for another way or more praxis kits.

Edit: Because of the age of the game we can only estimate, but the general consensus is there are 22 to be found in the world and on a near perfect playthrough of the game 40 can be unlocked through experience. So 62. Just shy of the 68 needed to fill all slots.

There should be a vent that leads to the other end of the hallway behind the turret (where the advanced hacking tutorial is made available). There's also a number of cardboard boxes in the vicinity. Just grab some and stack them up in front of the turret so it cannot see into the hallway. The turret won't see you as long as you stay behind the crates.

After you obstruct its view, you could then return to the other end of the hallway and make your way into the room.