It is very easy: just stop giving her anything in the sippy cup other than milk; and don't give her a bottle. She WILL begin to drink the milk from the cup. No problem.
When I was a Professional Nanny for two Doctors, the Mom being a Pediatrician, she mentioned one morning that she wanted her son off of a bottle completely by the time he celebrated his first birthday, he was 11 months at that time. I replied to her, if you want this mornings bottle to be his last then it will be his last. She said to go for it and I never gave him another bottle. I don't get the issues that parents have with bottles, sippy cups, pacifiers, baby sleeping in a crib, etc.
A book by Dr. James Dobson: All of his books are great; This book is titled: Parenting Isn't For Cowards.
About me: I am almost 54 years old, my dh and I have been married over 36 years, we have two adult kids, ages 31 and 28. They and their husbands have blessed us with eight grandchildren (the eighth is still in the "oven," a boy). I have been a childcare provider just about my entire life, beginning with babysitting cousins, neighbors and children from my church at age 12. I worked in a Day Care Center, was a Professional Nanny for many year and ran a Home Daycare Center so that I could stay at home with my children as they were growing up.