Notes

Can Grapple a character without needing to be close to them.
Those who die are instantly forgotten by the living. It's as if they never existed.
Shares mental saves (Int, Wis, Con) with a random party member when targeted, forcing them to make the save as well. Perhaps give this only a chance of occuring.
If they speak its name they take psychic damage, or must make a mental save against being stunned.
Roll percentile dice. Roll 1d6. From 1-50, the PCs have 30 seconds to decide who loses that many spell slots between them, or else they are lost randomly. From 51-00, they have 30 seconds to decide who regains that many spell slots.
The horror desecrates an area with a 25ft radius. All rolls made within the desecrated area (damage rolls, attack rolls, saving throws, etc.) are inverted (high rolls are bad and low rolls are good; 20's are misses and 1's are hits; attribute bonuses are applied as normal, so a longbow attacker may have +6 to hit, but that is a detriment when firing from inside the zone).
Transforming more and more mass around it into itself? Like imagine the horror when a weapon of the party slowly turns into tentacles.
The eldritch horror does not roll d20's, but 2d12.
Maybe let them change one letter in a spell? (Cause Fear -> Cause Bear) - Same w/ the horror
Another idea is to have a horror that makes players not notice when they take damage. Every single attack the horror makes, the party think is a miss, until they fall unconscious at which point they experience as if they lost all their hp in one hit (this would require you to keep track of each players hp and how much damage they've actually taken).
It can choose the damage type for attacks that don't make sense, as well as saves. You're bitten by a sharp toothy maw, make an Intelligence saving throw, and dealt thunder damage. Pierced by a cone of fire partially dodged by it missing your AC. Frozen solid by a bolt of lightning or resist it with a Wisdom saving throw. A psychic scream deals slashing damage unless you make a Dex save.
Grapple you with its tongue, which causes all healing to be nullified on the person grabbed.
Only Prime Numbers hit it. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31
Have the eldritch horror attack them, roll damage, but don’t apply it then. Instead, apply that damage later throughout the campaign. The reason why is because the eldritch horror is a 4th dimensional being whose damage can reach across time, which is a spiral.
I like the idea of attacking death saves while the target is still conscious. So whenever it hits have them do a save or fail a death save that will apply next time they go unconscious.
Whenever someone scores a hit on the horror, it immediately assumes the shape of a party member other than the one that scored the hit.
When they first engage it, everything seems roughly normal. As combat starts, you say, with no explanation, “ten.” A turn or two later, “nine.” Never acknowledge the countdown or any question about it. Combat continues as normal until you reach zero.
The terrain shifts and folds creating sheer walls where there wasnt before, the sky around them becoming neon green before instantly melting into a deep purple.
Physics shift and change and suddenly you can walk on walls and there are random points where gravity is backwards or just doesnt work at all (cant move, just drift in the direction they were moving when they entered the area until they reach the other side).