From the main menu, select 'Play Game' and Championship will be at the top of the list. Championship consists of 5 levels containing the hardest waves of all Areas. Therefore, Championship is a bit harder than any other Area (and also a bit longer).
However, you will start the Championship with a Galaga Trap (gives you additional satellites and support ships if destroyed). After the first wave, each time you lose a life, you will restart the wave with all the bonuses from the Galaga Trap.
Finally you are free to choose the difficulty so play on Easy and this should be a breeze. The trophy will be yours when you have beaten the Championship.