Successfully complete Single Player mode on the Easy or Normal difficulty to unlock the Hard difficulty.
When you start, you will be in a room with a plasma cannon and an RPG. Grab them both, then tap the activation panel to enter the Boss room. After a short cutscene, the fight will begin. Start by using any desired weapon other than the RPG or sniper to destroy the four crystals around the room. Try to avoid the Boss' attacks, as they do a lot of damage, especially the laser that it fires from the middle. When the crystals are destroyed, fire at the center of the Boss (where it fires the blue laser) with the RPG. When it is destroyed, it will keep doing the attacks that it did when you entered the room. Destroy the four other crystals on the Boss with either the plasma cannon or RPG. When they are destroyed, a cutscene will play and the game will be completed.