It isn't quite hard to find out one after intensive playing and Google searching. I ended up mailing the game author about the other one. Here are both of them.
1. Unlock the 8th ship
In the "Select Ship" menu, there's a question mark at the last slot. Complete the campaign in all three difficulties and a ship will appear at that place. It requires all 9 gold, silver and bronze medals to unlock, with 36 defense and 140% speed.
2. Complete the advanced tutorial
According to the game author, the tutorial will become an advanced version (called a "warm up") after completing the campaign in any difficulty. The advanced tutorial contains three stages, introducing waves of marching cubes and motherships.