All must be acquired in the fourth chapter and you must have Mustadio in your party for these to work.
Beowulf - Read the rumors at Goland, and go to Lesalia. Beowulf will be there. Agree to accompany him to Goland. Battle along side of him and he will join.
Biblos - Clear all ten levels of the Deep Dungeon.
Cloud - After Reis becomes human again, visit Goug. Cloud will run to Zarghidas. Finish Igros and follow Cloud to Zarghidas. Win the fight to recruit him.
Construct 8 - Rescue Reis from Goland. Go to Goug. Worker 8 will join following a cutscene video.
Dragon Reis - With Beowulf, go to Goland. Fight a series of battles and after Reis is rescued, he will join.
Human Reis - Read the rumors at Zeltennia. Buy a flower in Zarghidas. Then go to Goug. There'll be a battle in Zeltennia - towards the end of that fight Reis will turn into his human form.
Have a character be a level six Chemist and a level six Squire.
Master Knigh and Black Mage. Get Level 8 for Dragoon, Ninja, Geomancer, and Samurai. And kill 20 enemies in battle so that the enemy disappears off the grid - three round set.
Here's what you need to do in order to unlock a job:
Archer - Squire (Lv. 2)
Arithmetician - Black Mage (Lv. 5), Mystic (Lv. 4), Time Mage (Lv. 4), White Mage (Lv. 5)
Bard* - Orator (Lv. 5), Summoner (Lv. 5)
Black Mage - Chemist (Lv. 2)
Dancer** - Dragoon (Lv. 5), Geomancer (Lv. 5)
Dragoon - Thief (Lv. 4)
Geomancer - Monk (Lv. 4)
Knight - Squire (Lv. 2)
Mime - Chemist (Lv. 8), Dragoon (Lv. 5), Geomancer (Lv. 5), Orator (Lv. 5), Squire (Lv. 8), Summoner (Lv. 5)
Monk - Knight (Lv. 3)
Mystic - White Mage (Lv. 3)
Ninja - Archer (Lv. 4), Geomancer (Lv. 2), Thief (Lv. 5)
Orator - Mystic (Lv. 3)
Samurai - Dragoon (Lv. 2), Knight (Lv. 4), Monk (Lv. 5)
Summoner - Time Mage (Lv. 3)
Thief - Archer (Lv. 3)
Time Mage - Black Mage (Lv. 3)
White Mage - Chemist (Lv. 2)