A bear levels up when you receive a duplicate. Every event gives only certain bears as a reward. If you'd like to level up different bears, consider playing an event which offers different bears as a reward. So, for example, if you want Stretch Bear to level up then you should play a lot of Chapter 1 events since that is where Stretch Bear can be won.
This is how you can know which bears are awarded in a particular event: https://spryfox.zendesk.com/entries/70141190-How-do-I-know-which-bears-I-can-win-from-an-event-
This is how you go back to previous chapters: https://spryfox.zendesk.com/entries/69624864-How-do-I-move-between-chapters-