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