You committed a blunder by not making a rent agreement with your tenant. In the absence of a written agreement you might face some hurdles in the court in your pursuit to get her evicted. Having said this, you do not have any other remedy. Hence, now file a case for the eviction of your tenant in the court after issuing a legal notice through your lawyer to her. If she does not leave after the legal notice is issued to her then you may file a case for her eviction in the court.
We cannot tell how much money it will consume as your advocate alone can tell you what will be his legal fees. It will be unwise to tell the time frame within which the court will decide your case as it depends on the pendency of cases in the court, the efficiency of judge,etc. Initiate the legal process now if you want to have a favourable outcome quickly. You need to bear in mind that you do not have a written agreement with your tenant, so the longer you allow her to stay without commencing the legal process the more difficult it can be for you to bring her out. Time is of great essence in such cases.