Here is the full list of all 35 SOULVARS achievements.
Complete M01_Suzaku City
Complete M02_Soul Contact
Complete M03_Collapsing Gate
Complete M04_Gate Signal
Complete M05_Sudden Crisis
Complete M06_Under the Ground
Complete M07_SoulCage
Use Slashing Arts 200 times
Use Thrusting Arts 200 times
Use Striking Arts 200 times
Use Shooting Arts 200 times
Use Fire Arts 200 times
Use Cold Arts 200 times
Use Wind Arts 200 times
Use Elec Arts 200 times
Use Land Arts 200 times
Use Healing Arts 200 times
Activate Soulflow abilities 100 times
Use Mods to enhance your gear 50 times
Drink BulletCoffee 20 times
Drink PowerCola 20 times
Drink PsychoSoda 20 times
Drink MuscleDew 20 times
Drink GeekLatte 20 times
Drink PolarisWater 20 times
Drink HabaneroSoda 20 times
Drink PenguinSoda 20 times
Drink ElecSoda 20 times
Drink TornadoEnergy 20 times
Drink GraceOfEarth 20 times
Run from battle 50 times
Rest for a total of 50 hours
Reach an Anomaly Gate Score of 10,000
Close the Soul Prison Gate
Close the Pandemonium Gate