Answer:
Climbing = Gerund
To skydive = Infinitive
Won´t let her = Infinitive
Waking hours = Participle
Are spent = Past Participle
Explanation:
Climbing is the noun (and subject in this case) formed by the gerund of to climb.
To skydive is the infinitive with preposition to linked to the verb wants and is the object. What does she want? To skydive. I´m not sure but I think it functions as an adverb, because it adds something to the verb want.
Won´t let her is an (accusitive) infinitive functioning as an adverb.
Waking hours is a participle that functions as an adjective to the noun hours.
Are spent is the past participle of to be.