The goal is to complete achievements, which usually involve collecting a particular plant. As soon as the "Achievement complete" message appears, allow you bee to die. You can then move on to the next achievement.
Control
Other than challenges that require rapid tapping, it is easier to control the bee with short taps and holding your finger on the screen.
Obstacles
Do not worry about colliding into flowers or other objects. There are no obstacles that will block your progress.
Positioning
Try to keep the bee towards the left side by collecting as many flows flowers and moons as possible.