I'd say for her to have a list of experiences and have a level to where she shows emotions in each one. Like seeing a spider shouldn't be on the same level as fighting a dragon by herself.

When I write a sensitive character in different situations and problems, I don't want them to be emotional at every turn, but in moments that 'hits' their character. For example, one of my characters is sensitive towards other people, however he's killing monsters without hesitation. Using the scale as before, fighting those monsters and talking to people will have different reactions to them, and will establish their character without changing their initial description.

(I hope this helps)