For this achievement you'll need to have 1,000,000 Units at once (not cumulative). This really sounds more time-consuming than it is, partially thanks to the game's latest updates.
Get a weapon for your ship and fly out into space. Somewhere in your current solar system, there should be a space station. Find the asteroid field nearest to it and keep blasting asteroids there until either your inventory is full, or someone launches an attack on you. When that happens, fly into the space station and sell your freshly mined materials. Repeat until you become a millionaire. :)
Using this method, I was able to get the achievement within 20 minutes.