Here is the full list of all 32 Solar Flux achievements.
DELIVERE 90% PLASMA IN A SINGLE SHOT
COMPLETE A MISSION WITHOUT USING ANY FUEL
SURF BETWEEN 2 PLANETS WITHOUT THRUSTING
USE PLASMA TO COLLECT AND DELIVER OTHER PLASMA
RIDE 3 FLARES IN A ROW WITHOUT THRUSTING
RESTORE A SUN TO 100% EQUILIBRIUM
COMPLETE ALL 'TUTORIAL' MISSIONS
COMPLETE A MISSION WITHOUT TAKING ANY SHIELD DAMAGE
SAVE ALL OF THE MAIN SECTORS
SAVE ALL OF THE BONUS SECTORS
WIN 3 STARS IN ALL 'IGNITION' MISSIONS
WIN 3 STARS IN ALL 'VOYAGER' MISSIONS
WIN 3 STARS IN ALL 'SOLAR PRISM' MISSIONS
WIN 3 STARS IN ALL 'EVOLUTION' MISSIONS
WIN 3 STARS IN ALL 'BEYOND' MISSIONS
WIN 3 STARS IN ALL 'ASTEROIDS' MISSIONS
WIN 3 STARS IN ALL 'FORCE FIELD' MISSIONS
WIN 3 STARS IN ALL 'ORBITAL' MISSIONS
WIN 3 STARS IN ALL 'THE ABYSS' MISSIONS
WIN 3 STARS IN ALL 'METEORS' MISSIONS
WIN 3 STARS IN ALL 'MINES' MISSIONS
WIN 3 STARS IN ALL 'RICOCHET' MISSIONS
WIN 3 STARS IN ALL 'CRONUS' MISSIONS
WIN 3 STARS IN ALL 'FLUX' MISSIONS
WIN 3 STARS IN ALL 'DARK STARS' MISSIONS
WIN 3 STARS IN ALL 'ODYSSEY' MISSIONS
WIN 3 STARS IN ALL 'THE VOID' MISSIONS
WIN 3 STARS IN ALL 'HELIOS' SECTORS
WIN 3 STARS IN ALL 'OCEANUS' SECTORS
WIN 3 STARS IN ALL 'HYPERION' SECTORS
WIN 3 STARS IN ALL 'CERBERUS' SECTORS
WIN 3 STARS IN ALL GALAXIES