Eidolons não podem usar armadura mesmo depois de fazer proezas de proficiência.
Do site do d20pfsrd:
Armor Bonus
The number noted here is the eidolon’s base total armor bonus. This bonus may be split between an armor bonus and a natural armor bonus, as decided by the summoner. This number is modified by the eidolon’s base form and some options available through its evolution pool. An eidolon cannot wear armor of any kind, as the armor interferes with the summoner’s connection to the eidolon.