So, let’s suppose I have a character wearing an ashigaru armor (armor value of 3). During battle, her opponent manage to hit her with enough opportunities to also inflict a critical. The total damage is 5 and the deadliness of the weapon is 7. So where does the armor apply? On the 5 damage which means she will only take 2 fatigues? Or on the crit wound which would reduce it to 4 (before rolling for fitness)? Or both?

Resistance (which is what armour gives you) reduces the fatigue you take when you defend.

It does not affect critical strikes except for odd niche abilities (the Hida Defender's school ability, for example)

So if you're attacked by a damage 5, deadliness 7 weapon, and your opponent gets (and spends those opportunities on a critical strike), then if you defend you will take 5-3=2 fatigue, but will still suffer a severity 7 critical strike (less the result of your fitness check)

Everything Magnus said mirrors my understanding of the rules as well. One detail not mentioned in the original post, however, is that damage comes in two varieties, physical and spiritual. You may already know this, but it's worth talking about in case any new players are reading this. In the example above, if the damage inflicted was physical, the ashigaru armor would reduce fatigue inflicted by 3 since ashigaru armor works against physical damage. If the damage inflicted were spiritual, however, the ashigaru armor wouldn't reduce the fatigue inflicted and the character would suffer all 5 fatigue. In either case, the character would still suffer an additional critical strike of severity 7, as Magnus described. Sanctified robes are one of the few pieces of equipment I can think of that offer resistance to spiritual damage.

Perfect! Thank you for the clarifications.