Cut the minute up in parts and narrate the evolution back to your player.
RAW I agree with Icyfire's answer, however, this is not how I would rule it when running the game.
Since the battlemaster is observing the target actively and knows about these things, they should be able to assess that the target is getting better and better defended. Only giving the player the information at the end of the minute seems to be doing them a disservice when they should be rewarded for using the feature in a smart way. As such, give them time to act during the change in AC:
- Player: I observe my opponent and try to assess his weaknesses using my class feature
- DM: You catch your opponent in the midst of his preparation for the upcoming fight, he has already put on his bracers, but his breastplate still lies on the floor at his feet.
- Smart Player: I take advantage of this and attack, focussing my attacks on his obviously unprotected chest.
Result: the AC counted is as it was at the beginning of the minute (you could go further than this by having an actual gradual climb in the AC over time, but I feel like that would take you too far).
If the player decides not to act in that moment and lets the target get ready for the fight, follow Icyfire's answer and give them the assessment as given by the feature at the end of the minute.