Answer:
<em>Climbing = </em>Gerund
<em>To skydive </em>= Infinitive
Won´t <em>let </em>her = Infinitive
<em>Waking</em> hours = Participle
Are <em>spent </em> = Past Participle
Explanation:
<em>Climbing </em>is the noun (and subject in this case) formed by the gerund of to climb.
<em>To skydive </em>is the infinitive with preposition <em>to </em>linked to the verb <em>wants </em>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 <em>want.</em>
Won´t <em>let</em> her is an (accusitive) infinitive functioning as an adverb.
<em>Waking </em>hours is a participle that functions as an adjective to the noun <em>hours.</em>
<em>Are spent</em> is the past participle of <em>to be.</em>