Use brief taps to send Lumpy Space Prince to his destination in order to not block the screen and make things less confusing. When first starting and your spotlight is very small, position yourself in the center. You will have a better chance of escaping when needed, without missing any targets that get close. After your spotlight gets larger, you will be able to work from closer to the edges. As levels get faster, use vertical movements to catch your target.
Power-ups
Try to get speed and heart power-ups when they appear. The speed power-up will allow you to catch up from any missed opportunities caused by grabbing the boost. The heart power-up slows time and features a score multiplier. The time and energy power-ups are less important but will are still helpful. Ignore the disco ball power-up, unless it appears at the start of a level and you have a smaller spotlight.