In every stage, you get a medal based off the score you receive in two ways:
1. Collecting as many Coins as possible by exploring the stages and finding them.
2. Get rewarded a few of them in the end of the stage based off how fast you completed it.
I'm not sure how many you need to get a bronze, but i assume it would be around 2000 Points or less. However, even if you get a Silver, Gold or Platinum, you can still get the achievement for the Bronze.
Warning: This game is pretty glitchy in terms of the achievements, most of the time, you'll only get 1 achievement after you beat a stage, even though a lot of times, you'll should have gotten multiple at once. So i don't recommend going for a lot of achievements until you get a good chunk of the easy ones, but for the Bronze Away! Achievement, you should get this after playing any stage for the first time.
If you're having trouble with the achievements popping, beat the Daycare Dash level as Buzz and it will force the achievements to pop (for whatever reason), you'll need to unlock Buzz in Daycare Dash first, so don't worry about collecting achievements for now, just enjoy the game for a while and then go for the achievements.