A hypothetical exercise in abusing the Natural Attack rules.
A Ragebred skinwalker can get two hoof attacks and a gore (with Extra Feature, you can pick up both).
Getting Bite/Claw/Claw is easy, either with the Feral Mutagen or Lesser Beast Totem/Animal Fury (or adopted for that bite attack trait).
So at level 2 (via the Alchemist path), you can end up with Bite/Gore/Claw/Claw/Hoof/Hoof, 6 natural attacks (4 of which are primary, hooves being secondary).
Am I missing any other easy to get natural attacks?
Unfortunately you'd miss out on the gore/hoof/hoof by any other race.
You can get a gore from a helm of the mammoth lord, so races with stuff better then two hooves might be preferable.
True, though that becomes affordable around lvl6-7, and I believe the aasimar wings are also secondary. Unless you get the hooves back from something else, but the wings come in later too. Natural attacks are better the lower level you are, since you're cheating BAB iteratives.
On the other hand, with so many primary attacks, you may be better than iterative since you don't take iterative penalties. Nice.