Here is the full list of all 26 Gensokyo Odyssey achievements.
Wake up for school
Complete the tutorial
Defeat Marisa Kirisame
Defeat Kogasa Tatara
Defeat Yuyuko Saigyouji
Defeat Remilia Scarlet
Defeat Kakkoi and Utsuho
Defeat Eirin Yagokoro
Defeat Cirno
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
Accept Kakkoi's bribe
Become Eirin's Apprentice
Get arrested by the FBI in the lamest way possible
Solve the Bone Riddle
Remember one tiny piece of information
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