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