The rainforest is a part of the spa and there is a charge.
You can do it just for a day. It was $15 per day unlimited.
You can also get a week pass or if on the Wonder a 3 or 4 day pass. It was $50 for the week when I was on, but I believe it is now $75.
On the Magic, as the cruise went on, they advertised different passes. Such as, if you went on day 4 of the cruise, you could get a 4 day pass for a better price than $15 per day. I don't know if they still offer this.
When I went, the rainforest was only crowded once during the week. Although I liked the heated tile lounges in the main room, I preferred the heated tile lounges in the sauna like room to the right of the main door. The seats are pretty hot in there so I recommend that you grab a towel or robe to sit in/on. There is a hose to sprinkle on the seats if you want to cool it off more, just don't soak everyone else in there!