Flicky is a pretty straight forward game, getting this trophy is a little harder. The goal of the game is to get a number of birds and turn them in. However you get more points based on the number of birds you turn in a time. Up to about a ten thousand points
But beyond that you get points based on time. If you complete the level FAST, and by that I mean around 15 seconds) you get 20k. Plus the bird bonus is about 30k. You should be able to get 60k on the first two levels after a couple attempts and then play conservatively after that.
In addition there's bonus levels after every other level. I was never able to do it perfectly but I imagine there's a big bonus (in the 10-20k range) for that as well.
It took me only four stages to get this, and the key was beat the first two stages perfectly and as fast as possible.