As mentioned, once you have all five of the multipliers building up to 10 billion studs should go fairly easily and quickly while you finish off other achievements.
However, one caveat/bug, to be aware of. If you complete the bonus level (where you get to destroy everything in LEGO Land as Sauron) for the following achievement:
in this particular LEGO game it will count the 1 million studs you get in that level as part of your total, but does NOT count them toward earning the achievement. Thus, every time you do the bonus level you have to collect a million more than you think to get this achievement. For example, if you complete the bonus level one time prior to unlocking this achievement, this achievement will not unlock until you reach 10,001,000,000 studs rather than the 10,000,000,000 the name implies.