Undead and contructs are immune to any attack requiring a fort save that doesn't affect objects. But both suffer the effects of critical hits and can be staggered.
I've always played animated objects as immune to critical hits. Thus they would be immune to Staggering Critical due to being immune to critical hits. They are not immune to being staggered if by some means other than a critical such as a spell.
I'm leaning towards immune to Staggering Critical. They are already immune to most of the critical feats being immune to stunning, exhaustion, and the like. Dazing Assault and Staggering Critical have always been one of those gray areas. You can daze and stagger creatures immune to stun. That's why I see a lot of fighters choose Dazing Assault over Stunning Assault.
I'd like to hear how others run it.
Animated objects are constructs and have construct immunities. They are not immune to critical hits. (You can snap a books spine, and break a chairs legs :p) They were immune in D&D 3.5. But this is Pathfinder.
Staggering Critical requires a fort save. So they are immune to Staggering Critical (or at least the full effect of it.)
Avianfoo is correct: While constructs\undead are not immune to crits in general, they are immune to Staggering Critical since it: allows for a Fort save to negate; and does not specifically state it affects objects.
Avianfoo is correct: While constructs\undead are not immune to crits in general, they are immune to Staggering Critical since it: allows for a Fort save to negate; and does not specifically state it affects objects.
Indeed. And it sucks.