Learn Croatian: Ja bih ispunio tvoju želju.

We use the conditional mood, which is made of two parts: the helper word bih (meaning "would" for the "I" form) and the active past participle (or l-participle) of the main verb, which is ispunio.

Can I drop the pronoun Ja in this sentence?

Yes, it is very common to drop the pronoun! However, because bih is a clitic (a "weak" word that cannot start a sentence), the word order must change. If you drop Ja, the sentence becomes Ispunio bih tvoju želju.

Would the sentence change if a woman is speaking?

Yes. The participle ispunio acts a bit like an adjective and must match the gender of the speaker. A male says Ja bih ispunio, but a female would say Ja bih ispunila.

Why do tvoju and želju end in -u?

They are in the accusative case because "your wish" is the direct object being fulfilled. The base feminine words tvoja (your) and želja (wish) both change their -a ending to -u in this case.