Adam's meetings with Mejia all occur automatically through normal story progression. After the first meeting in the B Block showers, Adam must find and meet with him in solitary confinement. Upon using the emergency security override system that allows Adam to open the cell, a conversation with Mejia ensues. When Adam inquires about Wilburg's murder, Mejia will claim ignorance. Nevertheless, if Adam has evidence to the contrary, he will automatically confront Mejia. Mejia will then admit to committing the murder and the achievement will unlock.
The information needed to refute Mejia can be found in two pocket secretaries. The first has information about a suspicious schedule change request. You find it when you enter Processing and search the drawers to the right of Orin Kepac's computer. The computer is inside one of two office areas of a large shelter that spans the processing area. The drawers may appear to be blocked by an inmate who moves over in front of them but they can still be searched. The second pocket secretary has information about an automated security console being hacked to target Wilburg and suggests that Mejia was the hacker. This pocket secretary is in a safe in the Automated Security Office. To ensure the achievement unlocks, make sure you access Adam's database and read these two pocket secretaries either when they are acquired or at some other point before you confront Mejia.
Attached is a video guide for the achievement edited to avoid story-related spoilers except for those implied by the achievement description. It starts right after the first meeting with Mejia that occurs automatically through story progression:
There is some optional evidence, too--a hacking device near the crime scene, Wilburg's corpse with heart removed, and an augmented heart--presumably Wilburg's since it was recently removed. The additional evidence is not required for the achievement but is part of the larger story surrounding the goings-on in the prison. Moreover, although these are clues, they are not necessarily evidence that directly refutes Mejia:
The above video shows how to get the two required clues and two of the three optional clues. The third optional clue is picked up earlier in the video that accompanies this guide:Solution for Smooth Like Soap In Deus Ex: Mankind Divided