Here is the full list of all 25 Touhou: New World achievements.
Follow Reimu to the moon (Marisa Story).
Have an important talk with Yukari (Marisa Story).
Head to Hell for the first time (Marisa Story).
Head to the Outside World for the first time (Marisa Story).
Reach Level 40.
Complete the subquest "The Ultimate Battle".
Raise any Skill to Level 10.
Deal 10,000 damage or more at once.
Complete the subquest "The Strongest in Gensokyo".
Reach Spell Level 4.
Complete the main story.
Save up 500,000 gold.
Head to space in a rocket (Reimu Story).
Use Kogasa's Smithy for the first time.
Reach Level 20.
Deal 2000 damage or more at once.
Have an important talk with Kasen (Reimu Story).
Reach Spell Level 2.
Use the Power Amplifier to increase your number of heals to +3.
Raise any Skill to Level 4.
Finish your first subquest.
Defeat Kokoro (Reimu Story).
Achieve a 100-hit combo.
Achieve a 50-hit combo.
Head to the Outside World for the first time (Reimu Story).