Here is the fragment again:
To see her favorite part of the parade, the majorettes with their twirling
batons.
You correctly identified the fragment as an infinitive phrase. To see, the infinitive beginning the phrase, is the clue.
To fix this fragment, you could add a subject and verb, modifying the item like this:
After much waiting, Amy saw
her favorite part of the parade, the majorettes with
their twirling batons.
Or you could use Punctuation Rule 5:
Main Clause + Ø + Infinitive Phrase.
The correction would look like this:
Hopping as high as she could, Amy tried
to see her favorite part of the parade, the majorettes
with their twirling batons.
Yet another choice is to use Punctuation Rule 6:
Infinitive Phrase + , + Main Clause.
And the correction would look like this:
To see her favorite part of the parade, the majorettes
with their twirling batons,
Amy pushed her way to the front of the crowd.
Enjoy riding that beautiful horse!