I would suggest therapy first, and I think both you and your H/DD have valid points. She wont change until she's ready. However, it may be that once in therapy, she'll be willing to work with someone who is not Mom. Once she gets comfortable, she may be more willing to take risks and start to work on it with a stranger who does not have a big stake in it. I've done that myself- claim I dont want to do something because I am scared, but in private, with a therapist who is non judgmental and supportive and not vested in the outcome, admit that maybe it was something I might want to work on, and we did, slowly. The idea of changing itself can be scary.
I wonder if it would help if you explained the reason for therapy differently- maybe, that its ok if she has these fears, but its not ok with you that you have to alter your schedule and activities so drastically to accommodate them, and you want to go to therapy so you two can find a way for you to work together. So she's not going to change her phobias, per se, but to work on how they effect you, and your relationship. She might be more willing since you aren't demanding she change the phobias, and once she gets into counseling, she might see that working on them could help. Or she might not, but come up with ways to keep her phobias, and not inconvenience you. She might also learn ways to manage her anxiety herself- so while it makes her anxious to go to bed herself, she could maybe learn to handle it.
Or, you could simply say that you are worried about her and her anxiety, and you want her to feel better. That you hope going to therapy will help her with that, but she can use it as she wishes. A good therapist may be able to steer her around to the phobias in a non-threatening way. Or, it could be theres an underlying issue she wants to work out first that will help the phobias in the long run.
Overall, I think you might have a lifestyle clash- if your DD lived someplace where she didnt have to swim or go boating, never went near caves and butterflys were few and far between she'd be ok. And really, those things aren't that hard to avoid. I'm not saying YOU should, just that if she keeps them, when she becomes an adult she can choose a lifestyle where they really wont bother her. I think fear of fish really isnt that uncommon. I've known several people who were scared of fish- some to the point they refused to swim at all except in pools. And fear of bugs is also not uncommon.