You need to have a total of 20 ships on screen at the same time. This would be quite challenging to do under normal circumstances, but fortunately there exists some techniques to make this easy.
Basically you just exploit the large yellow ship (see "Master Pilot" for this technique) and the large green ship, either together or separately, depending on exactly what spawns. Cluster the small stationary yellow ships in a corner of the screen, as many as possible. Use the large green ship to quickly create small green ships that follow the same path. Just work with what spawns. See the image below for an idea of what this can look like. I have 15 small yellow ships in the top left corner, and have started spawning small green ships. I could easily get 25 total ships or more on screen with this set-up.
NOTE: The long snake-like chains of yellow ships only count as ONE ship on screen, regardless of how many ships make up the chain (though they do count as multiple ships for scoring and multipliers). This makes these the worst when going for this achievement. Get them landed as fast as possible.