The Peaks is the fourth world in the Career mode. In order to reach the Peaks, you must complete the Highlands, Forest, and Canyon worlds by reaching the boss track and crossing the finish line.
1) For the Highlands and Forest boss jumps, you don't actually have to go off the jumps and land them to travel to the next world. Simply ride around the obstacles and cross the finish line.
2) Take it slow, and remember you don't have to follow the path of the track or go off any stunts to complete any level.
3) Complete the easy bonus objectives (such as "Get _ seconds of air time" or "Reach _ kmph") and avoid attempting difficult bonus objectives. This will award you extra lives.
4) Take a direct path to the boss track and choose easy difficulty tracks and medic camp tracks if discovered.
5) The Canyon is the only boss jump that must be completed to reach the Peaks world. The Canyon boss level has a giant gorge in the middle of the map which must be jumped over and landed to reach the finish line.
The video below shows how to land the jump efficiently (Canyon jump starts at 1:30). Also, speeds in kmph not mph as I wrongly stated.