Inquisitor is an achievement/trophy in Metro 2033 and Metro 2033 Redux, awarded for killing two demons. The kills that need to be obtained can be earned at any time throughout the story line and do not need to be obtained in one play session. This can be earned quite early in the game on the levels Dead City 1, and Dead City 2. On Dead City 1 a demon is feeding on a dead stalker's body and can be killed quite easily if it is hit with a sticky grenade. The second one that can be killed easily is in Dead City 2, when it lands behind Artyom and Bourbon near the end of the level, and can be killed quickly with a few over-pressurized shots of a Tihar. The Outpost level has more demons if you missed the earlier chance.
Inquisitor is a reference to the Spanish Inquisition during the Middle Ages and Early Modern Period when there was a lot of superstition concerning people having demonic powers and using witchcraft. Inquisitors were the ones to "end the threat" (usually by killing the suspected "demon").
Inquisitor is also likely a reference to the Inquisitors of the Warhammer 40k Imperium, who also often kill demons. This is furthered by the fact that Warhammer 40k games Dawn of War and Space Marine were licensed to THQ which also made Metro 2033.
Attempting this on the level Alley is not advised, because as soon as the first demon is killed a second one will quickly follow.