I own 25% share of a Hawaii condo with my parents' living trust which owns 75%. I live in the condo, and currently pay AOAO & maintenance expenses along those ratios. My parents have agreed to let me rent it out and receive 100% of the rent. Would we have to declare 75% of the rent received as a gift? If so, is there some way to do it without being considered a gift?

I think this is more a tax question than a real estate question and I'm no tax guy. That being said, if your parents aren't involved in collecting any money, you collect it all and handled the rent collection it is not a gift. You could own none of it and they allow you to rent it out its still 100% your profit and your tax liability. Consult a tax guy once they come out fom under the tons of junk they are handling right now.

Rental income is never a gift, trust or not. If you keep all the rents, you pay tax on all of it, minus expenses.
There is no way around it.
Keep in mind that renting it eventually turns it into an investment property, so you should plan to live there 2 years out of any of the last 5 before selling, if you ever sell, or you will be stuck paying capital gains.
You might want to consult a tax adviser.