Here is the full list of all 37 Natsuki Chronicles achievements.
Played Training Stage 1 in Story Mode.
Obtained an A to A++-Rank for a stage on any difficulty in Story Mode.
Obtained an S-Rank or higher in Story Mode.
Cleared Stage 1 in Story Mode.
Began Story Mode.
Cleared all stages on every difficulty in Story Mode.
Played a stage on hard difficulty 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.
Played Arcade 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.
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.
Checked the online rankings after playing Arcade Mode.