My PCs have an upcoming bottle with an Elder Polyp (Tome of Horrors III 10). The monster is copied into an adventure path I'm running and has 4 tentacles. The Elder Polyp does not have Combat Reflexes or a similar feat that provides attacks of opportunity, but it does have 4 tentacles.
Should each tentacle be given its own attack of opportunity, or would it still only be one attack of opportunity per round for the creature?
One attack of opportunity a round.
Consider a player playing a hypothetical broody drow dual-wielding matched scimitars: if they asked for two AoO because they have two swords, you'd probably say no without hesitation. The Polyp is no different: lacking any special abilities that say otherwise, merely having extra attacking limbs doesn't grant more than one AoO.
If it does not have combat reflexes and does not state anywhere in the stat block that it gets extra attacks of opportunity, it only gets 1.
The Flying polyp has 4 tentacles and specifically needs combat reflexes to give it more opportunity attacks: http://www.d20pfsrd.com/bestiary/monster-listings/aberrations/flying-polyp
