Here is the full list of all 36 FreeCell Quest achievements.
Reach Level 10
Unlock a second Free Cell.
Reach Level 5
Win your first battle.
Reach Level 20
Reach Level 40
Complete a 2 suit level in less than 10 seconds.
Complete a 4 suit level in less than 60 seconds.
Complete a 6 suit level in less than 120 seconds.
Complete a 8 suit level in less than 300 seconds.
Unlock a third Free Cell.
Unlock a fourth Free Cell.
Unlock a fifth Free Cell.
Unlock a sixth Free Cell.
Complete Principate of Harkhares
Complete Khanate of Sebassaher
Complete Heptarchy of Nepherkeb
Complete Kingdom of Eidolon
Complete Republic of Serenil
Complete Kingdom of Melaan
Complete Principality of Niverlunn
Complete Kingdom of Renmark
Complete Kingdom of Segakorn
Complete Kingdom of Seth-Ar-Gol
Complete Seignory of Ghordrun
Complete Great Lands of Asteria
Complete Kingdom of Saverne
Complete Kingdom of Hurlen
Complete Arkheinate of Sidjev
Complete Pirate Nation Archios
Complete Palatinate of Isorion
Complete Lands of Linoë
Complete Free City Ulshantir
Complete Bastion of Krell
Complete Condominium of Saadaran
Complete the entire continent of Selvarin!