First off, you're going to need some money in your Swiss account to actually pay to upgrade the skills. You'll get some money in the process of playing the campaign, but Swiss money can be made by having a Customs Office with the "Special Tax" activated, having a Bank(s) set to "Slush Fund", hiring Moneygrubbers as managers for some of your higher-budget buildings, etc.
If you're in the late-late-game, repeatedly researching "Research to Swiss Account" is a good bet. With 3 Science Labs, 3 Observatories, a Library, a College, two Clinics, a Hospital and a Space Program all maxed out and researching I was getting "Research to Swiss Account" every 15-16 months or so. About 5 years of doing this while slushing money and "Special Tax"-ing my exports netted me like a quarter of a million dollars in my Swiss Account - plenty for this achievement.
Now, there comes a catch. You can only upgrade each dynasty member once in a mission before the price goes way, way up. There's a fairly painless way around it though.
Play the quickest game you possibly can. Sandbox game, starting in Modern Times. Set the win condition to Construction: Space Program. Load up the game, upgrade your dynasty member (or members if you feel so inclined, but you only need to get one of them to level 5) and save. Be sure to overwrite your old, not-upgraded dynasty if prompted. Then quick build a power station of some kind, and then build your Space Program.
Donezo. You just "won" a mission, and can now start up a new sandbox game (using the same file if you wish) and upgrade your dynasty member again for the low, low price of 10, 20, 30, or 40k, rather than 100k or whatever exorbitant amount it goes up to. Shouldn't take long at all to do this four times, provided you have the Swiss Account money.