Not Grigori is hostile, therefore you must kill him to progress. Killing him drops a ration from Half-life 2,
which you can feed to the Curse detector in order for it to gain healing abilities. To summon not Grigori, you must obtain:
5 dolls "which can appear upon destroying 5 globes spawned around the map", 1 skull, and one "AlyxDoll". Upon completing the NotGrigori Ritual Not Grigori himself will spawn infront of the table where the skull, 5 dolls and AlyxDoll float.
The more you do the ritual, and the more you keep up on killing Not Grigori, Not Grigori will start to get harder and harder when it comes to killing him.
Which is why you should have the Curse detector with you at all times when it comes to killing Not Grigori.
How to summon up NotGrigori
Follow the instructions here: Notgrigori Ritual
1) Initial: cone upgrade 1;
2) Manhack madness: cone upgrade 2;
3) Bomberman: final cone upgrade.