After the events of Prey’s "Reboot" and, obviously, assuming you save Mikhaila Ilyushin as part of "Assist Mikhaila Ilyushin," she will make her way to your office in the Talos 1 Lobby. You’ll find her hanging out there with Dr. Igwe and January. Just showing up at your office will complete the "Mikhaila Ilyushin" objective, which is why we’re including it here. But talking to her will get you a new optional objective, "Mikhaila’s Father." Mikhaila’s looking for information on her father and, uncomfortably, you might know something about him. Or, well, you might have used to know something about him. Before your brain got all Swiss cheesed.
Access the Volunteer Archive Terminal in Deep Storage
From your office, head up to the Arboretum, then down into Deep Storage. From there, head up the stairs on the right toward the data vaults and Danielle’s Sho office like you did during "Restore from Backup."
You need to get into the Confidential Records room. It’s to the right of the Data Vaults. You can hack your way in with Hacking 4 or you can climb up and over the wall. Climb the data drives in Danielle’s office and run across the cable racks the same way you did to get into the data vaults during "Restore from Backup."
Erase Yuri Andronov’s final audiolog entry or Transfer Yuri Andronov’s final audiolog to your office workstation
You’ll enter Yuri’s Test Subject ID automatically when you get to the computer. After you listen to the audio file, you’ll have to decide what to do. You can delete the evidence right now and never let Mikhaila know what happened (you monster). Deleting the entry will end this objective. If you decide to fess up, you can transfer the file to your computer in your office. Mikhaila won’t listen to it until you get there (because otherwise it wouldn’t be uncomfortable enough).
Listen to the Yuri Andronov’s final audiolog with Mikhaila in your office
Head back to your office and pull up the recording you transferred. It’ll be on your computer under Utilities. (If it’s not there, talk to Mikhaila first and it will appear.) This uncomfortable act will earn you the "Self-Incriminating" achievement/trophy and close out the "Mikhaila’s Father" objective.