Amulet of Mighty fists + eidoloen

[Khorus]

So I make an amulet of mighty fists (speed)and put it on my eidoloen, does it apply to all his natural attacks?

[Agita]

If you mean whether the enhancement bonus applies to all its natural weapons, yes. If you mean the Speed property, no, because you can't put it on an Amulet of Mighty Fists in the first place. In this case, you want the Necklace of Natural Weapons.

[veekie]

Actually, seeing as hes speaking of Eidolons, I assume it's for Pathfinder

Yes you can do that

This amulet grants an enhancement bonus of +1 to +5 on attack and damage rolls with unarmed attacks and natural weapons.

Alternatively, this amulet can grant melee weapon special abilities, so long as they can be applied to unarmed attacks. See Table: Melee Weapon Special Abilities for a list of abilities. Special abilities count as additional bonuses for determining the market value of the item, but do not modify attack or damage bonuses. An amulet of mighty fists cannot have a modified bonus (enhancement bonus plus special ability bonus equivalents) higher than +5. An amulet of mighty fists does not need to have a +1 enhancement bonus to grant a melee weapon special ability.

[fuinjutsu]

not that it matters, because unless pathfinder changed how speed works, you still only get one extra attack.

[veekie]

Well, yeah, you'd need something else(read: a hell lot more expensive) to get an extra attack on all your natural weapons.