This achievement is story related and cannot be missed. It unlocks, during your third playthrough, when you gain control of 9S inside the structure at the beginning of Chapter 17--The Tower. Moreover, in spite of the fact that the description states that the moments must be watched, the achievement will pop regardless of whether the records are viewed or not. The records are in the form of a text adventure with a few pictures. They tell an interesting story so the records are well worth watching even though the achievement will unlock if you decline to view them.
To gain entrance into the structure, you must first, follow the story, and obtain keys for each of three small structures. Once you have gained access to these three substructures, go to a nearby City Ruins access point like the Resistance Camp, City Center, or Near the Tower and
make a save. You are doing so for two reasons. First, in case the achievement glitches, you can use this save to remedy the issue. Second, there are two 'bad' game over endings that are obtained by not following the story. Once you make this save follow the story. There are cut scenes that occur as you enter the structure and some other content. Following this, you regain control of 9S. This is the point when the achievement should pop.
Since there is an achievement for obtaining all endings, this is a good opportunity to get them although you could also use chapter select that becomes available after you finish the third playthrough. The achievement for achieving all endings can also be bought at the special achievement shop that becomes available after your third playthrough is complete. It costs 50,000. This achievement is not available for purchase because it is an unmissable story related achievement that is unlocked before the achievement shop becomes available.
If the achievement does not unlock when you regain control of 9S inside the structure, you most likely have experienced a glitch.. In the event of a glitch, clear the cache. To do so, turn off the console by holding the
button on the console for at least ten seconds and then unplug the console for at least 20 seconds. Load the save you made after gaining access to the three small structures. Clearing the cache will most likely remedy the problem and the achievement should unlock when you regain control of 9S inside the structure following the cut scenes and other content.
The two bad game over endings you can earn just before this achievement or later through chapter select are the S and V endings:
*** Spoiler - click to reveal ***Earn the S, city ecape, ending by leaving the tower area after Devola and Popola make their appearance.
Earn the V, reckless bra[V]ery, ending by fighting the enemies with Devola and Popola instead of hacking the tower door. Their energy will eventually run out.