Hi!
When I switched DD to cups (I actually did this at 10.5 months b/c I was afraid it would take forever and it didn't so I was trying to do it before she turned 1 LOL) I just kept offering her a sippy cup instead of a bottle for the morning...and still bottles later. She eventually took to it and I just then dropped any bottles except her night one...which I did last. When I was ready, I switched up her routine, gave her a sippy cup at night downstairs and then brought her up to brush teeth, read a story and go to bed.
To switch from formula to cow's milk I did it mixed. So 3/4 formula to 1/4 milk...and gradually increased over the course of about a week or so. Then when it was just milk...she didn't like it cold as formula had always been room temp. So I stuck it in the microwave for like 10 seconds tops...just to take the chill out. She did well with that and then was slowly able to drink it cold.
Some LOs just take to it easier and some will stick their heels in and stubbornly refuse to drink it. If she's drinking water and eating dairy (cheese, yogurt, etc.) then I'd be willing to let it go if she doesn't drink much at first out of the sippy cup. If you give her a bottle if she refuses to drink from the sippy cup, she'll keep refusing and hold out for the bottle. So...hopefully she will take to having milk feeds in a cup easily, but if not, and she otherwise eats well and won't be dehydrated b/c she'll drink water....don't stress. She will be fine if it takes her awhile to come around.