This page may not speak to your particular situation, but we give this advice often enough that we figure it's worth writing down in an FAQ.
It's not impossible
There are multiple players who have completed the campaign on Normal difficulty, and at least one player who has completed the entire campaign on all three difficulties.
You have to do Bear School
Playing very well will get you into possibly the third chapter or so. After that you won't be able to progress without leveling up your bears, which is largely done in Bear School.
There are basically only two levers for scoring higher
Your score is basically the product of:
- How well you play without considering the bears' score bonuses.
- Your bears' score bonuses.
Score targets are set according to how well we expect a player to play and how strong we expect the score bonuses to be. To some degree, strength in one aspect can compensate for weakness in the other (e.g., playing better than expected can make up for having weaker bears than expected, or vice versa). But only to a degree.
If you're leaving rocks on the board, not maximizing the special tiles, etc., then maybe playing better will help. However, if you are playing as well as possible and still not winning, then score bonus is the only other lever you can move (not counting Boosts, getting luckier with the random letter generator, etc.).
Invest in the higher-rarity bears
You get more bang for your buck/honey/coffee if you invest in higher-rarity bears because their score bonuses scale better as you level up. For example, a Level 80 Legendary IOU Bear would have higher score bonus than a Level 220 Epic Equistribear. So if you're lucky enough to find a bear of higher rarity than your current best bears, invest in it because eventually it will carry you farther than your current bears will.
The difficulty bar may not have to be green
If the only thing stopping you is the color of the difficulty bar and you haven't attempted the mission yet, go ahead and give it a try--hopefully you'll win, and if not you'll at least see how far away you are. Please see this page for more information. However, this is more of a tip for, for example, if you're at the end of the game or on a mission where you'll win a new bear; otherwise you're kind of just kicking the can down the road because the missions get harder as you progress and eventually you'll get to a mission that you can't beat.
Strategies for some particularly tricky missions
Please see this page. Unless you want to try to figure these missions out for yourself first, in which case maybe you shouldn't look there just yet.