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