Pac-Man Championship Edition DX

Each of the stages has a set number of Time Trials (A few Short ones & one Long one) you must complete. The "Time Trial" is a longer version of the short ones (and usually includes a lot of those in them) and has a higher number of apples to get collected to finish it. Best advice I can give you is to watch the patterns of the small pellets and the locations of the ghosts as these normally will give you a good idea of what patterns to run in order to give yourself the best time possible on them. Also, do not be afraid to use your bombs if you need to in order to avoid dying at first. If you run out of bombs, don't worry because they will be replenished if you do end up dying (just make sure you don't run out of lives before you finish). Here is a list of stages and how many Time Trials:

Championship II: 10 Short Ones & 1 Time Trial
Highway: 9 Short Ones & 1 Time Trial
Junction: 12 Short Ones & 1 Time Trial
Spiral: 9 Short Ones & 1 Time Trial
Manhatten: 10 Short Ones & 1 Time Trial
Dungeon: 8 Short Ones & 1 Time Trial
Championship I: 9 Short Ones & 1 Time Trial
Half: 21 Short Ones & 1 Time Trial
Dark: 8 Time Trials

Just keep practicing them and once you complete all of them, the trophy will pop after that!