Hmm...
At the moment, you have to do Story Missions to unlock Free Mission, unless you find a completed game save file (I think there are some over
the internets ; maybe you can ask here, on PSOW, on Clementine...).
Here's what you unlock by completing Story Mission (each time in C-A rank) :
Chapter 1 :Clyez City Linear Line Platform・Fight for Food
Holtes City Flyer Base・Plains Overlord
・The Mad Beasts
・Sleeping Warriors
Chapter 2 :Ohtoku City Flyer Base・Flying Beast
・Moonlight Beast
・Hill of Spores
Chapter 3 :Dagora City Flyer Base・Desert Goliath
・Awoken Serpent
Chapter 4 :Holtes City Flyer Base・The Dual Sentinel
Clyez City Space Dock・Dark Satellite
Chapter 5 :Holtes City Linear Line Platform・Endrum Remnants
Chapter 6 :Dagora City Flyer Base・Mine Defense
Chapter 7 :Holtes City Linear Line Platform・Train Rescue
Chapter 8 :Ohtoku City Flyer Base・Rainbow Beast
・The Holy Ground
Chapter 9 :Ohtoku City Flyer Base・Grove of Fanatics
・White Beast
Chapter 10 :Dagora City Flyer Base・Desert Terror
Chapter 11 :Holtes City Flyer Base・Scarred Planet
Holtes City Linear Line Platform・Electronic Brain
Clyez City Space Dock・Seed Awakened
And S rank to every unlocked Free Mission.
***
And though it's not officially possible to download additional contents, thanks to Agrajag, you can download some missions (cf.
this).
Here's what it contains :
Mission Pack 1 :・The Black Nest C-S3
・Citadel of Sand C-S2
・Bladed Legacy C-S2
Mission Pack 2 :・SEED Express C-S3
・Beach Bum Beast C-S4
・Snowcap Screamer C-S4
Mission Pack 3 : Planes, Trains, and Automobiles(note: does not contain planes, trains, or automobiles)・Floader Rush
・Lunga Rodeo
・Striking Out
Mission Pack 4What killed the dinosaurs? The ice age!・Frozen Woods C-S3
・Temple of Ice C-S3
・Absolute Zero C-S3
Mission Pack 5: Dawn of a New Day・Sinners’ Banquet C-S3
・Castle of Monsters C-S4
・Distant Dream C-S4
All of this is available at the Commune Club (GC 3rd Floor)