Slayer Gates are extremely difficult Doom: Eternal encounters. In them you are transported to another reality where you fight against a seemingly endless wave of demons using the extra ammo and lives you have on your person. If you don't have enough, you reload at the next checkpoint, and sometimes you come out with barely any bullets. However, you must complete them all to complete the Demonic Corruption Meter and to unlock a final weapon.
You can find a Slayer Gate near the end of the Cultist Base mission. That's right before I use the train to enter the Terrordome to kill one of the priests. You find him in the room where you have to knock down the giant statue to smash a hole through the wall and use it as a bridge to the next room. You want to take down the statue first before going after the killers gate.
After knocking down the statue, look to dig to the left of it. You should see a wall that you can grab if you pull down. Do it and grab the wall. Look behind your position to see a yellow bar. Double down on it, but hold your dash. After swinging off the post, use your jump to grab the wall on the other side. You shouldn't have to use your dash to reach these two places, but it's a useful safety net if you need it. Turn back to your current position and you should see a dash box. To reach the other side of the wall, you will need to use your dash and the cartridge to reach it.
Once there, go up the wall and enter the upper platform. You need to grab the yellow and swing even further, and the Killer Key should be there for you.
The door of the killers is not far. The door that originally blocked you from the key should open, allowing you to enter the room where you smashed the statue. Turn right, behind the block you used to lift off the ground to reveal the jump boost, and you can access the killers door. Good luck fighting it.
There are six keys and slayer doors in Doom: Eternal. You need it to unlock a weapon hidden in the Fortress of Doom. You can repeat these encounters during mission selection, but you won't get another key upon completion. You cannot access or acquire killer keys or doors if you play a mission with cheat codes enabled.