Here is the full list of all 37 Natsuki Chronicles achievements.
Checked the online rankings after playing Arcade Mode.
Played Arcade Mode.
Cleared all stages on every difficulty in Story Mode.
Played a stage on hard difficulty in Story Mode.
Began Story Mode.
Cleared Stage 1 in Story Mode.
Cleared Stage 2 in Story Mode.
Cleared Stage 3 in Story Mode.
Cleared Stage 4 in Story Mode.
Cleared Stage 5 in Story Mode.
Cleared Stage 6 in Story Mode.
Cleared Stage 7 in Story Mode.
Cleared Stage 8 in Story Mode.
Cleared Stage 9 in Story Mode.
Cleared Stage 10 in Story Mode.
Acquired 500,000 CR in Story Mode.
Acquired new weapons in Story Mode.
Acquired 3 or more new Primary Weapons in Story Mode.
Acquired 12 or more new Primary Weapons in Story Mode.
Acquired all Primary Weapons in Story Mode.
Acquired 3 or more new Secondary Weapons in Story Mode.
Acquired 12 or more new Secondary Weapons in Story Mode.
Acquired all Secondary Weapons in Story Mode.
Acquired 3 or more new Special Weapons in Story Mode.
Acquired 6 or more new Special Weapons in Story Mode.
Acquired all Special Weapons in Story Mode.
Started a stage in Story Mode with Ex.Shields equipped.
Started a stage in Story Mode with 5 or more Ex.Shields equipped.
Started a stage in Story Mode with the max number of Ex.Shields equipped.
Obtained an A to A++-Rank for a stage on any difficulty in Story Mode.
Obtained an S-Rank or higher in Story Mode.
Played Training Stage 1 in Story Mode.
Played Training Stage 2 in Story Mode.
Played Training Stage 3 in Story Mode.
Played Arcade Mode more than 20 times.
Cleared all stages in Arcade Mode.
Started Arcade Mode with custom settings.