Here's a guide for completing Daycare Dash without falling, this also doubles as a guide for Say It With Rockets
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 this achievement, you'll probably only get it after replaying the levels once or twice, or explore the stages a ton during your first playthrough.
If you're having trouble with the achievements popping, beat the Daycare Dash level as Buzz and it will force the achievements to pop, you'll need to unlock Buzz in Daycare Dash first, so just enjoy the game for a while until you get most (if not all) of the easy achievements, you might even get a Gold or Platinum by accident.