Here is the full list of all 21 Wish Project achievements.
Clear a stage without getting killed.
Earn at least 100000 score during a single stage.
Collect at least 400 score items during a single stage.
Destroy at least 400 enemies during a single stage.
Destroy at least 25 squads of enemies during a single stage.
Destroy at least 1200 bullets during a single stage.
Destroy a boss phase in 3 seconds or less.
Clear a stage with max power level and bomb stock.
Earn a Gold Medal on any stage.
Clear the game on at least Normal difficulty without using any continues.
Clear Boss Rush mode on at least Normal difficulty.
Clear Shotless mode on at least Normal difficulty.
Earn all six Gold Medals with any character on at least Normal difficulty.
Clear the game using Radius on at least Normal difficulty.
Clear the game using Eve on at least Normal difficulty.
Clear the game using Trigger on at least Normal difficulty.
Clear the game using Kettle on at least Normal difficulty.
Clear the game using Waltz on at least Normal difficulty.
Clear the game using L.C. on at least Normal difficulty.
Clear the game using Cotton on at least Normal difficulty.
Clear the game using Sign on at least Normal difficulty.