All data thanks to the awesome post by OmegaRisk at GameFAQs.
For anyone on the Japanese or an altered US version (AR code or (J) version access) of Star Force 3 working their way through the Secret Satellite Server, I tossed together an easy-to-read chart showing the progression path along with the code for each level (Hint: US version with access to SSS can't view the last letter of any code given in-game) along with a sidebar list of the required card for advancement
If something from the chart doesn't work, it means I'm an idiot and inserted a typo somewhere. Check the post linked above and try using the information there instead. Note that some cards in the sidebar are not listed by the translated US name but nothing was too hard to figure out once you access the specific folder. If you're playing the (U) version and don't yet have a Satellite Server entry in a Brotherband slot you can load your save in the (J) version, enable the Lv. 1 Server, save, and access SSS like normal. Also, there are AR codes floating around that perform the same function. See other posts around this and other forums for further details.