I think the "Solitude and Sorrow: Final Base" achievement is currently NOT obtainable. There's a conflict between Audrey, Aletta, Palla, and Cassidy that makes it so you always keep at least one of them, so you can never get rid of every girl. To clarify:
For Aletta, you can only get rid of her apparently when you fail the prerequisites for "The Aftermath" event after finishing Cassidy's story. You can also fail the Office harem showdown after not becoming CEO but then you're stuck with Shiori/Lavish (as you need to get rid of both before this point in the story). I see no other way to make her leave forever in the wiki, but maybe I missed something?
For Cassidy, you can choose to never meet her (which makes you unable to get rid of Aletta), or fail the investigation getting Dwayne fired (same result), or lose her during the Bitchy harem showdowns (leaving you stuck with Palla and/or Audrey). If you fully complete and record the investigation and allow Aletta to handle Dwayne, you can get rid of Aletta but you're then stuck with Cassidy.
For Audrey, you can choose to never meet her (which makes you unable to get rid of Cassidy if you finish her story), or fail the Bitchy harem showdown (leaving you stuck with Palla/Cassidy). I see no other way to get rid of Audrey in the wiki that isn't the Bitchy harem showdown.
For Palla, you can ditch her when she invites you to the club, or failing the Bitchy harem showdown after that point in the story (leaving you stuck with Cassidy/Audrey).
Any tips? What am I missing?