Just checking we played this correctly, because it was ridiculously easy. He doesn't engage with anyone and doesn't have retaliate.
So basically he never attacks unless you specifically engage him? You can just attack him forever and never get hit (just the occasionally Writhing Appendage, which are pretty bad.)
You cannot 'engage' Cnidathqua as he is not considered at your location, but his effect does allows investigators to attack him despite not being at the location.
The only instances in which Cnidathqua attacks are 1. when Agenda 3a advances, or 2. when an elder thing (the alien-looking) token is pulled from the bag. The attack from the Agenda advancing is against every investigator in play, while the attack from the token is only against the player performing the test.