If she is drunk at work, or her alcohol use is negatively impacting her work performance - then follow your company policy, plain and simple.
If there is not a clear policy, discuss with your higher-ups and seek advice on the performance management plan they advise.
If you can clearly see that her alcohol dependence is the root of the problems, then also refer her to any mental or substance abuse health benefits your company may offer; part of a manager's job is to ensure that employees in trouble get the support they need. There are programs (i.e. short term disability, socially-funded rehab, etc) that may be available in your area as well.
Do the 'right' thing by the individual by trying to align them with help to the extent you are able. Be forthright with the individual about how alcohol is impeding their work performance. Give the warning(s) and support you have latitiude to give, but beyond that if it continues you must write her up, refer her to management, or take any other appropriate actions including dismissal. Her alcohol problem is not YOUR alcohol problem.