These tips have been tested in every difficulty, HOWEVER, Nightmare difficulty does ramp up the senses of the Alien A WHOLE LOT. It's reccomended that you take your time when playing Nightmare while also taking this tips with a grain of salt. That being said, have fun dying a lot in Nightmare.
Pro Tip: Play on Hard. It's difficult, and you will die, but it's the way the game is supposed to be played. Totally worth it.

Simply put, confidence is key. Don't be afraid to use the little bit of wiggle room that this room gives you with the Alien AI to get through tough sections. In the first hospital section, I found myself constanatly in the same rooms hiding from the Alien. Don't let yourself do that. KEEP MOVING. The tips at the bottom of the loading screens won't lie- the more you move, the more the Alien has to cover.

There's a reason that this game emphasises stealth- you'll die if you don't utilize it.
Which leads me to my second point- how to stealth in this game.
Don't use lockers.
Don't. Use. Lockers.
These Devil's Broom Closets lock you into a loud, tight, and very sight restricting space that the Alien will almost undoubdetly catch you in if you've hidden in it when he's closer than .40 on you motion sensor to you.
Also, don't trust that breathing mechaninc. I feel like the devs only put it there to assure the player that they're gonna be safe. Turns out that about 50% of the time, Mr. Baddie still opens up that door and noms at ya brains.
So, instead of the lockers, use desks. They're more present, they're large, and they allow you more room to see the Big Dude trolling the ship. It pulls you down about another 25% of the way that the normal crouch doesn't allow, and you can lean into the sides of the desk with your ctrl key to super hide from his view. That being said, you can still die from these. I just seemed to die a whole lot less when using these desks.

Walking. It's that magical thing that you do in this game when you're not crouching and you're not running. Turns out, Mr. Alien doesn't discriminate between crouching and walking that much when he's not suspucious. Did the Big Guy just pop down from the rafters and give you a big fright, but he's not looking your way? Great! Walk away. Crouching will slow you down around 30%, which could lead to you, once again, becoming mince meat.
Seriously, use the walking thing. Especially when he's up in the ducts. There is no discrimination. Equal opportunity killer, and what not.
Feel free to try to use the 'Stealth Walk' too! I used this a lot in my original playthrough without even realizing how effective it actually is. Here's a video of another player showing how effective it is:

It's accurate. Most of the time. I guess.
But you seriously don't need to use it as often as you think you do.
The sound design in this game is masterfuly done to the point that once you get some of the key sounds that the Alien makes down, you should know almost exactly where he is.
Also, it attracts him hardcore. My finding were that whenever the Sensor was below .50, he would notice the noise and quickly come to investigate.
If you don't hear noises, simply do not use the Motion Sensor.
It either means that no one is there, or that some one is there, and the've stopped moving. In which case, refer to the point above about sound, because if they hear your sensor, you're probably boned. Wait a few seconds, and, if you hear nothing, keep moving.

Judge a room or area before you go into it. If you don't hear the Alien up in the ducts, you already have an advantage. Your goal at this point is to simply stay quiet, walk around, and complete your objective. Don't hit stuff with your wrench. Don't aggro that random Working Joe. Just keep moving, and mind your own business.
Also, assess where you are with your supplies and what chapter you're in. Certain chapters don't even feature the Alien (Chap. 8 being the best example). If you feel like you've made a ruckus and you've been making all kinds of noises and the Alien still isn't showing up, you're probably in the green. Keep on keeping on.

Respect the Alien.
It's here to kill you.
Respect Amanda.
She's there to GTFO.
So just GTFO. (Collect stuff as you go, though)
The game is built so that the more agressive you are, the more agressive the Alien is. The more passive you are, the less likely the Alien is to adapt to your play style.
Seriously, respect that fact.
Twoards the end of the game, I found myself constantly using the Flamethrower because I had a stupid amount of ammo for it.
Yeah, not a good idea.
Come the second to last chapter, and the Alien basically didn't care that I just shot fire at it's facething. Basically 10 seconds after he scuddled into the vents, he was right back up in the room.
Respect the Alien.
Leave the Alien alone.
And just maybe, maybe, you'll make it off of Sevastapol.