This will be a grind, folks. But there is one thing you can do to make it much easier.
Post-update: With a new drone and a new super added, your total should be 844,000 when you get this achievement if you upgrade all 12 drones / supers). Geoms collected in Ultimate mode and Hardcore mode also count for this achievement.
Play through Adventure Mode to at least level 10 (Ruby). Completing this level will give you a "collector" drone, which will fly around the level collecting geoms for you, in addition to ones you fly over yourself. For added effectiveness, do not spend any geoms on upgrades until you get this drone. Depending on skill, you might be able to upgrade it two or three times by the time you get it.
If you are also going for
though, don't even worry about grinding it out as you will get a large number of geoms just trying to pull that task off.
As for the grind itself, that's going to depend on skill and player preference. Keep track in the Adventure mode of which stage you get the highest multiplier on (if you miss it before the game ends, just look at how many geoms you earned in your "bank".) If you've not progressed far through the campaign too far yet, Level 11 (Peanut Dreams) and Level 17 (Rock) are good choices. If you've gotten further along in the campaign, 35 (Endurance), Level 42 (Running in the Family), and Level 49 (Super Sequence) are better options. Again, this will depend on skill, so if you're getting more geoms consistently in another level, go with it.
Note, despite being a secret achievement, this will show you your progress in the Achievements app. Only geoms collected in adventure mode count, and assuming you've upgraded everything, you should be able to get this achievement when your adventure mode count hits 870,000. (13,000 geoms to fully upgrade each drone / super, 10 drones and supers in total)
(Thanks to K4rn4ge and Smallywood for suggestions)