it says after the first time, so does that mean the first action is fine, then the next time he is targeted he would have to discard a card? if he has no cards to discard does that mean he cannot target this unit with actions?
Eternal Armor
A topic from AEG's L5R CCG Rules forum, copied for Oracle of the Void from a copy of the forum saved in October 2015, so pages it didn't save are missing. Players' names are left out; the rules officials are named. Rulings are as they stood on these dates; later rulings, the rulebooks and the Rules Archive may differ.
it says after the first time, so does that mean the first action is fine, then the next time he is targeted he would have to discard a card?
No, 'after' means 'immediately after'. What really matters is that another player's Battle action targets the Personality with the Armor attached for the first time this turn. Immediately after this happens, the trait triggers and gives the action the additional cost, "Discard a card."
if he has no cards to discard does that mean he cannot target this unit with actions?
Yes, not voluntarily. If he targets another unit and the targeting changes to the Personality with the Armor attached, the action's effects do not happen (see Interference with mandatory costs).