鏡の監視人 (Mirror of Observation) 10
Holdout to the end until Mirror Shield self-destructs.
Mirror Shield is one of the mid-bosses, who appears during AREA 11. All you need to do is dodge its attack pattern which loops four times. Dying at any point during this fight will void the achievement (to be confirmed).
Just to confirm, you can actually die during this battle and you will still get the achievement.