To get this achievement, you must control 10 T-3 planets with three colonies, with every building/turret space filled. This does not include colonization tools, such as Bio Protectors and Uber Turrets.
Of course, you'll need to have lots of money! Conquering or buying planets from alien empires will help with achieving the badge. If you have the Staff of Life or the Safari Vacuum, that will help your progress towards the badge.
Purple Spice sells for the highest price (up to §73,096), with full stacks of 99 selling for millions that can easily fund the buildings, simply hoard all of the local planets that produce purple spice, and look for a planet that will buy it for a high price. Pink and green spice also sell for moderately high prices, and are more common on planets than purple spice.
Using other saved game that have further progress in the space stage to boost your planet's terrascore can save you time and money.