In order to unlock Rad Mode, you must first complete every amateur and pro challenge. Yes, even the 50 spin one in Neon City Pro 3...
Rad Mode is basically a perfect-only mode. Only perfect grinds and landings are permitted; sick, ok, and sloppy ones will cause you to automatically bail.
It does seem tricky at first, but once you get moving on the levels, they tend to get easier since a lot of the later levels can be done in fewer combos. Perfect grinds are easier to hit than the perfect landings present a lot more in earlier levels (besides base).
I have put together a video containing completion of every level in Rad Mode. Notably tricky ones are Junkyard 3 and 5 Pro, as they require very precise slowdown techniques in order to pass in this mode.