How much of Brazil should we see in one trip?

My girlfriend and I are looking to travel to Brazil next year for 2 weeks We are both active and want to explore and experience Brazil as much as we can. We would like to explore Rio, Ilha grande and the Amazon.

With the different climates and distance would you say this is possible and If so what month would you recommend. It looks like such a beautiful country we want to see as much as possible.