To get this very quickly, pause the game and enter the redbricks screen and enter the following cheat codes (They DO NOT disable any achievements)
Score x2 Multiplier N4NR3E
Score x4 Multiplier CX9MAT
Score x6 Multiplier MLVNF2
Score x8 Multiplier WCCDB9
Score x10 Multiplier 18HW07
Turning on all of these will multiply your stud counter by 3840, thus making it rather easy to reach 4 billion studs. The achievement will not unlock until you return to the bat cave after reaching the max counter.