Check your laws to find out the time line you need to give a tenant who's lease is about to expire. Then notify the tenant that you are not renewing the lease and she must vacate the premises on date xyz, by way of a certified letter.
If she is a month to month tenant, you can ask her to leave, given the proper amount of notice through a certified letter.
This is a perfectly legal and acceptable way to get a tenant out of your building. Remember, you need not give her any excuses or discuss that she is a nuisance to everyone in her path because that just opens up the conversation for debate as you defend your tenants. You need not explain yourself to this lady who is making everyone's lives miserable. However, if you must, make up a little white lie, like the apartment needs new plumbing or you are renovating the floors or restructuring the walls, she may be more inclined to realize she cannot stay there.
As a landlord, it is your duty to provide your tenants with quiet and peaceful enjoyment of their rental domain. Good for you that you recognize this issue. Everyone will be so relieved when she is gone, especially you because you will no longer have to deal with all of the complaints from her and the other tenants.
EDIT: maybe, if you can justify it (say, her apartment is in needs repairs), substantially raise her rent if she is a month to month renter. In the future, call previous landlords of your potential tenants and ask about how they do or do not play well with others.