Slayer Gates are the gated-off rooms with a portal inside. There are six of them spread across the levels (so not every level has one!) and every one of them is locked by a key that you need to find. They will appear on your automap with a purple colour in the area where it is.
The levels that contain the Slayer Gates are:
Super Gore Nest.
Once you find the key and unlock the gate interact with the portal to be transported to another area. Here you will fight a large group of demons of varying strength. Defeat them all and you will be transported back to where the gate stood. Once there you will find an Empyrean Key. Walk over it to pick it up. You can use this in the Fortress of Doom to unlock the Unmayker when you have all six keys.
Some things to keep in mind:
If you die in the gate you will not get any ammo you spent back.
If you play through the game with cheats on, any cheat, you will not find any Slayer Gates.
I would suggest leaving this achievement until a playthrough on the lowest difficulty in which you get all the collectibles.