You have a few issues going on here and you didn't do yourself any favors.
If both parties are on the lease, as long as the rent was paid, why would it matter that the boyfriend moved out? If the rent stopped getting paid, you just evict for non-payment.
What kind of lease was it? Was it for a year or month to month?
What is a "lease termination letter"? Unless it is month to month you can't end the tenancy until the time is up as long as you are getting paid. (Unless of course all parties to the lease agree and sign it)
If you notified her you were terminating the tenancy at the end of August and she didn't move out, that is when you should have started the eviction process.
And if you notified her the tenancy was ending in August, why on earth did you send her a notice of rent increase? Especially since you say she is damaging the apartment and there is smoking and noise etc.
I think the best you can do now is send her a 14 day notice. If she pays the money though, the tenancy is back on and you may have to wait until February to evict if she doesn't move.
Sorry to be harsh.