I take my DD to a place that just does kids haircuts. They have seats made from old riding toys so she gets to pick which one to sit in. There's a TV at each station playing movies and she gets to pick out a prize and lollipop at the end. We make a big deal about how pretty she will be and praise her for cooperating.
DD got her first hair cut at 25 months by a neighbor who is a hair stylist and she freaked out the whole time. I waited several months before trying again and went to the kid's place instead. She did great and she's been fine ever since. She is now just over 3. And she needs haircuts, she has very fine fair that tangles easily and we need to keep it trimmed so it's not out of control - otherwise it looks all straggly and all over the place.
Maybe you could also let her see you get your hair cut and then she'll see that it's no big deal. Or see if holding her in your lap helps. Give her a prize at the end for being a "big girl".