100% destruction with Falcon 50 times (in Single Player Mode)
As you play you unlock uses of the Mighty Falcon. Once you unlock the Mighty Falcon, you can hold down to use it. You fling a beacon at the level and the Mighty Falcon shoots blaster bolts in multiple directions. You will get a score from 0-100% based on how much damage you do. If you get a score of 100% you will get a gold medal.
You get Mighty Falcons by earning stars, playing the game for consecutive days, playing multiplayer, and failing a level three times in a row. The number of times you can use the Might Falcon in a single level is either the number of birds you get in a level or the number of Mighty Falcons you have remaining, whichever is smaller.
After using the Mighty Falcon for the first time, you unlock Mighty Launch . After the first level you get 100% destruction on, you unlock Falcon Escape . After getting 100% destruction on a level 50 times you unlock Hyperspace . The menu where you choose the episode tells you how many times you have gotten 100% destruction in that episode. It is under the gold medal on the right and will say something like 20 or 40. Thanks to jimmylad for confirming you can get 100% on the same level 50 times for the Hyperspace trophy.