The basic requirements for a guaranteed path to get this achievement are:
1. Rachel survives until the end of the game and does not get infected.
AND
2. Rachel rejects both Eric and Nick in the confrontation scene where she makes her final relationship choice.
As with most missable achievements in the game, there are a lot of factors that affect the outcome, and many of the requirements for other achievements will negate this one. But these are the major points to keep in mind:
1. Rachel, Nick, and Eric must all survive until the scene near the end of the game when she makes her relationship decision. This means: cut the rope as Eric (let Rachel fall), tell Salim to surrender rather than hide as Nick after you take down the vampire together, don't save Clarice as Rachel, remember where Jason and Nick plant the explosives in the corridor and tell Eric and Rachel to go the other way so they don't get 'sploded.
2. After the relationship decision scene, Rachel must continue to survive until the very end of the game. (Eric and/or Nick should be able to die after this scene has completed, but that is not yet confirmed; I kept them alive all the way, just in case.)
3. Rachel should be mean/sarcastic/non-romantic in any conversation with Eric and Nick, and vice-versa. With Eric, there are many dialogue opportunities for this, but not nearly as many with Nick. In the opening scene at the base with Rachel/Nick, make sure she tells him that they need to put their relationship on ice. Basically, take every opportunity to bring all of their relationships down.
4. There are at least 2 opportunities for Rachel to be infected during the "Survive the Assault" scene in the Sacrificial Chamber, so they must be avoided. The first is when you're playing as Salim and have the choice to shoot the vampire that's about to attack you, or the one that's already attacking Rachel on the ground. Choose to shoot the vampire that's attacking Rachel, or she will be infected. The second is when the ancient warrior vampire is choking Eric. As Rachel, you'll have the choice to save him or flee. Choose to flee, or she will be cornered and infected.
The achievement will unlock right after the last QTE is successfully completed during the final attack.
If other factors that affect the achievement are discovered, please note them in the comments and I will update the solution.