Here is the full list of all 36 FreeCell Quest achievements.
Complete Heptarchy of Nepherkeb
Complete Khanate of Sebassaher
Complete a 8 suit level in less than 300 seconds.
Complete a 6 suit level in less than 120 seconds.
Complete a 4 suit level in less than 60 seconds.
Complete a 2 suit level in less than 10 seconds.
Complete Condominium of Saadaran
Unlock a sixth Free Cell.
Complete Seignory of Ghordrun
Unlock a fifth Free Cell.
Complete Kingdom of Seth-Ar-Gol
Complete Principate of Harkhares
Complete Bastion of Krell
Reach Level 20
Unlock a fourth Free Cell.
Complete Kingdom of Eidolon
Complete Kingdom of Hurlen
Unlock a third Free Cell.
Complete Free City Ulshantir
Complete Kingdom of Melaan
Reach Level 10
Unlock a second Free Cell.
Reach Level 5
Win your first battle.
Reach Level 40
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 the entire continent of Selvarin!