10 billion is a lot of studs even with the maximum possible multiplier of 3840, but by using a purple stud that you can repetedly respawn it can be done very quickly.
The stud in question is on the backside of the island near the Caradhras Eagle Statue (Lower Middle of the map). When you find the purple stud next to a skeleton collect it and walk towards the water. At some point, approximately by the LEGO rock you will see the stud respawn. If you use the Attract Studs red brick you don't have to walk more than a step towards the stud for it to be picked up. By wiggling back and forth across the line you can thus collect the stud about once a second which gives you tens of millions of studs every second and the achievement in about five minutes. assuming you have all the stud multipliers.