As the description says, just complete episode 4 on "Hurt Me Plenty" difficulty or higher. While "Hurt Me Plenty" may be the easier option, completing it on "UltraViolent" will help towards the Rampage achievement, and will save you having to play through the episode twice. Please note this achievement cannot be obtained in co-op, it has to be done in single player.
If you do decide to play through it on "UltraViolent", remember that saving the game often can help, especially if you don't know what you're doing. This is by far the hardest episode in the game, so remember to save every so often. There are a lot powerful enemies in this episode, including several Cyberdemons, and a huge amount of Barons. Finding all the secrets in levels can really help you out too, as they often contain extra ammo and health/armour boosts to put you above 100%.
The first 2 levels are easily the hardest, as E4M1 has no medikits whatsoever in "UltraViolent", and E4M2 has huge waves of enemies attacking you in close quarters, with little ammo and not very powerful weapons at first.
Thanks to DaveOwl, I can confirm that you don't have to complete the secret level (Fear) to get this achievement. And thanks to deutschZuid, I can also confirm that you don't need to complete this level to unlock the Rampage achievement. However, it is very easy compared to the first two levels, and the amount of ammo, health and armour it sets you up with can greatly help you out in later levels, so I'd advise doing it anyway. You can get to it from E4M2, Perfect Hatred. Watch the YouTube video to see how to get to the secret exit, as it is kinda hard to explain it accurately.
The secret level is pretty easy, and is a nice break in difficulty after the previous 2 maps. Save the blue armour and the soul sphere till you've killed everything, as it'll give you a great advantage in the next level. You should also make sure to grab the backpack, which is hidden in the wall directly opposite the exit teleporter. This'll double your ammo carrying capacity, and will give you yet another advantage in the following levels.
In the final level in the episode, Unto The Cruel, you have to explore a bit before you get to the Spider Mastermind. There is an area of the level where a lot of items are sitting on top of pillars, so don't be afraid to take these as it's the last level anyway. When you get to the Spider Mastermind, remember that killing it doesn't end the level instantly, as you have to walk into the big hole in the floor that it was standing near to finish.
If you're still having any trouble, feel free to leave a comment below or send me a message and I'll be happy to help you out as best I can.http://doom.wikia.com/wiki/Thy_Flesh_Consumed