D&D 5E Nearly unhittable monster with 1 hit point

[Blue]

It's voluntarily moving, which means opportunity attacks go off. Now, you avoided making it a reaction which would make it once a round (though that's what reactions are for), but even with a high chance of saving sooner or later it will fail. And it could chain several full-moves together. (Get attacked, move, trigger attacks of opportunity, move again, run past the wizad durign this who swipes with a dagger, etc.)

Make it hard to attack anyone with polearm mastery, since they OA when you move close.

How about area spells that damage when you start or enter them?

All in all, this seems a bit wonky. I'd give them reasonable HPs and use a reaction for their uber-dodge to allow smart players to think around it.

 

[Creamsteak]

You reminded me of this: http://imgur.com/a/Vbzze#3

 

[Dausuul]

This was my first thought as well. But, the spell magic missile targets the opponent and it seems like an attack to me. So, shouldn't it also trigger the critter's "escape feature".

If this were a published monster, the answer would be no; an attack requires an attack roll. Since this is a homebrew monster, it can work however you want it to work. However, it's a moot point since magic missile has a 120-foot range and the maniac only has a speed of 60. Even if it does trigger, it's unlikely to be able to get out of range.