Me and a friend moved into an apartment together. We have lived in the apartment for about six months. Every month my roommate is late with her portion of the rent. This month She chose not to pay at all, even though I had already paid my portion, and now we're facing eviction. I can pay her portion of the rent, as well as I can afford to live in the apartment on my own. I refuse to live in the apartment unless I can evict her, How can I legally evict her.

p.s She is on the lease, and I have already spoken to her about moving out, she has made it very clear that she's not moving out unless she is evicted as wells as she's not going to pay any money either.

Are both your names on the lease?
TALK to your landlord ASAP and tell the whole story. You can't really pay her rent, because then he can't evict her for non-payment (he doesn't care which of you pays). Ask if he will be willing to evict her only, write you a new lease when she is gone, and you will sign a promissory note now to cover her rent for what she owed while actually still there.
If he refuses, that is his right, and you both get evicted.

You said she is on the lease, therefore she has as much right to be there as you. Neither of you can evict the other. The only way you can get her out is if the landlord agrees to evict only her. And that may not be possible depending on local laws.

As Joy said if you pay her rent, then why should he go through the expense of evicting her? So you have to enter an agreement with him. That agreement will probably mean promising to pay the full rent after she is out including anything she didn't pay. It will also probably mean reimbursing him for the expenses of evicting her.

After she is out, you can sue her for whatever she didn't pay. But without the landlord's cooperation you are stuck.