Each of these traits will come into play at some point in a level. As you can obviously tell, the game is broken up into levels. Each level has an objective or a number of objectives that must be accomplished before the exit warp portal opens up. There are also power cells located throughout the world. These power cells will be used to repair EVO's body, so you will want to collect all of them in every level.
Every level also has a souvenir.
These are valuable items that usually appear someplace after you complete all the level objectives and collect all the power cells. Sometimes they are in obvious locations, and other times you really have to search for them. You can finish and exit a level without getting the souvenir, but they will pay off in the long run. A big part of this game is solving puzzles, which usually requires the use of the animals in some form or fashion. I will tell you a little bit about one of the puzzles you will encounter early on, just to give you an idea of what they are like without giving away too much of the game.