Hmm, if I want to go for a no alerts run, even though I'm terrible at being sneaky, what would be good to be prepared with?
I might go for a Big Boss, but I think a couple of dry runs on lower difficulties would be a good plan. One for learning how to be properly sneaky and one for learning how not to kill anyone.
There are a few places that worry me a bit with the no alerts. The opening of the game, the run through the market at the end of Act 2, the Crying Wolf fight with all the Frogs, and Act 5 in general.
Excellent idea!
Anyway, for the dry no alert run the first thing I would advise is that you take your time. You won't finish quickly but stay prone almost all the time, with a significantly high camouflage percentage. You want to develop a route through each area that has the line of sight with the enemy broken as much as possible. If you've a very good memory you'll remember the location of most enemies off the top of your head and, hopefully, the route they patrol and the timing. If not, learning these pieces of information should be of high importance. Another thing you won't want to do is rely on your tranquiliser. In most instances, use of the pistol is unnecessary and it is much easier to simply avoid the enemies altogether (there is some areas when it's safer to tranquilise the enemies though, the start of Act 2 immediately comes to mind).
Honestly, if you take the game at a slower pace (for the dry run), crawl (or crouch-walk) through areas with a high camouflage percentage, take paths that avoid the enemies' cone of vision, use only the tranquiliser pistol (when necessary) and save in each area until you've perfected them you'll find that you will drastically improve. If necessary (I usually advise against actually following it exactly though) look at the walkthrough in the original post, not to follow exactly but to get some ideas of how to go through areas, how to play in general and what items to use.
As for those areas, the opening of the game is quite difficult. Up to the meeting with the Mark 2 on Extreme are the easiest areas to get caught simply because you don't have the FaceCamo. The beginning of the Red Zone isn't too bad but the areas before that can be quite frustrating.
The marketplace is pretty simple though, if you finished the previous areas with enough health (if not you can try use Rock Me Baby to increase your health to the halfway point) you can simply run down the path straight ahead, dive at the Gekko when he goes to kick you (with proper timing you'll dive through the attack), turn left to the stalls, run to the end and then dive to the Gekko's right side (it is your left) to dodge his kick.
For Crying Wolf see the area listed to that in the OP. Basically, use smoke and stun grenades to trap her if you're confident and if you're not just crawl under the truck and snipe her (this can be very time consuming depending on how lucky you get).
For Act 5, this is an area where you use the tranquiliser pistol. At the beginning you dive forward into a crawl, equip the FaceCamo and stay lying down until you've a high camo percentage. Keep crawling forward until the Frogs jump down and headshot them. Run forward again and then dive into a roll at the boxes into the middle of the alley. As the Frogs jump down, tranquilise them. Stand up, run forward and dive again at the corner with the boxes and tranquilise the enemies and then keep crawling until the enemy appears at the other end of the alley. After you tranquilise her, stand up and keep running along the left (by the big cylinders) and wall press to get around the boxes. When there is a gap with what looks like a cloth material dive roll towards it and into a prone position. Tranquilise the enemies that jump down and then crawl to the exit. To avoid the Gekkos, well, you'll have to use your own judgement. Screaming Mantis is easy, use the Saiga on lethal bullets (because you'll probably be low on V-Ring ammunition), inject yourself immediately and then ONLY shoot the mantis doll with the Saiga, don't bother with Meryl (in any stage of the fight) or the other Frog Soldiers. Finally, the Scarab Tunnel can be bypassed with a Chaff Grenade.
The worst area however is Act 3: Bike Chase. Those three sections, I can absolutely guarantee you, will cause you more problems than anywhere else and there really is no easy way to beat it.
Just, before you go for your Big Boss run (or no kill/alert Extreme run), make sure you have the following:
50 tranquiliser bullets for everything (because it won't be your second playthrough you'll be able to get the emotion ammunition too!).
50 V-Ring ammo.
4+ Chaff Grenades before you start (preferably ten), you'll get two more at the beginning of Shadow Moses but won't have enough time to get them elsewhere.
Ten Smoke Grenades (and ten of each colour too).
Ten Stun Grenades.
Solar Gun (this will make the bike chase so much easier).
25 Stun grenades and smoke grenades for the Grenade launchers (note that you probably won't even use these).
The Anti-Material Sniper Rifle.
The Militia Uniform for the Middle East (so that you can equip it and just run through the safe house).
(Note that my ammunition count is probably wrong for some items as Extreme has a lower limit for ammunition than the other difficulties and I can't remember them off by heart)
If you have all them, you're definitely good to go.