How can I change colors in an Illustrator file without modifying other aspects?

I purchased a stock vector design.

I want to change the preset colors used in vector art and leave everything as it is. The object is made up of bunch of shapes.

As I try to change the colors instead of it looking nice and blended as it did when I have bought it. All I see is the shapes with no gradients or blends.

Since I am new, I do not know the simplest way to change the color "theme" without messing up the way it looks right now.

Is there an easy way to change colors of an exiting Illustrator file?