Here is the full list of all 26 Gensokyo Odyssey achievements.
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Defeat Cirno
Get arrested by the FBI in the lamest way possible
Defeat Eirin Yagokoro
Become Eirin's Apprentice
Defeat Kakkoi and Utsuho
Accept Kakkoi's bribe
Defeat Remilia Scarlet
Defeat Yuyuko Saigyouji
Solve the Bone Riddle
Defeat Kogasa Tatara
Defeat Marisa Kirisame
Complete the tutorial
Wake up for school
Defeat Son Biten
Defeat Byakuren Hijiri
Defeat Hisoutensoku
Defeat Reiuji Utsuho
Bring everything back to normal
Unite Gensokyo back with Earth
Take the Scarlet Devil Manion's hospitality for granted
Defeat Rin Satsuki
Get a thousand dollars in Blackjack
Get 50k in Blackjack
Somehow get one million dollars in Blackjack
Get a Jackpot during Kakkoi's fight