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