I've done it. It took a ton of memorization and preparation to do. Here are some tips.
- Memorize the Maps. Make sure you know where every health pack, weapon, ammo, secret location, and enemy spawn is.
- Only go where you need to, if you don't need to grab rocket ammo on E1M3, then don't.
- Rebind your keys in the setup program. I used W A S D with the Arrow Keys to turn.
- Circle Strafe... but keep awareness of where you're strafing.
- Don't waste ammo. You don't need to use the Rocket Launcher to kill a Sarge, so don't.
- Learn how to get the enemies to fight each other... this is relatively easy with strafing. Get between two of them, and if you time it right, one will fire and hit the other as long as you keep moving. They will then be fighting, and you can move on.
- Use number 6... a lot.
- Keep moving at full speed. If you stop moving, you're dead.
- Watch speed runs, and use those routes. The faster you get through a level the higher your chance of success is.
Ultimately, this is one of those feats that will take practice and a lot of failure before you'll be able to achieve it. It took me about 7 months of practice before I managed it, but it felt oh so sweet after I got through the first and second Episodes. I still haven't beaten Episode 3: Inferno, on Nightmare.