Legal Question in Real Estate Law in California

You can't evict someone because of their immigration status.

a notice to terminate tenancy and an unlawful detainer action

Eviction just like any other tenant if they are breaching their lease or rental agreement.

Do you have a lease with your tenant? Has the lease expired? If expired, then you have a month-to-month contract; and you can just give 30 days notice to termination of the lease and ask the tenant to move out. Thereafter, you can do an eviction/unlawful detainer action if the tenant refused to leave.

If the lease is about to expire, don't renew it. You will be renewing it on a month-to-month basis if you accept additional rent. If you don't renew the lease, you don't have to give any notice, and continued possession by the tenant is immediately unlaful and you can proceed with unlaful detainer procedures at once.

Immigration status does not affect the validity of a lease; anyone can lease or even buy property in the United States irrespective of immigration status, residence, visa, blue card, etc.

Thieu and Whipple are basically correct, but if she's been there more than a year you must give 60-days notice. Consistent late payment is grounds for eviction even if she is current on the rent, if she still has time left on a lease. If it is month to month, then all you have to do is give notice (30-days if under a year, 60 if over). If she doesn't move out after the notice you can still file an unlawful detainer regardless of if she is current on rent, as long as you don't accpet rent for the period after the notice time runs.