Can an animal companion gained with the Animal Ally feat take the bodyguard archetype?
Sure. Any A/C can, it doesn't matter how you got it.
Yes, the A/C you get via Animal Ally has the full suite of A/C abilities and can trade them in for any archetype.
By contrast, a familiar you get via Familiar Bond doesn't have most familiar abilities and hence can't take an archetype. By the time you get Improved Familiar Bond too it's too late to take an archetype.
Ah, when i checked the animal companion advancement table I completely missed the share spells feature and assumed it was a druid / hunter thing.
My mistake, thanks fuzz :)
Yeah, the cavalier is the odd man out here.