There are many ways to express this idea in common English, but unfortunately your example is not one of them. Consider as alternatives: process (without the "up"), absorb, mull things over, think things over/through, let the gears turn, reflect (or pause to reflect), chew on the idea, contemplate, soak up (as suggested by @Bee), and probably many more.
I think the phrase you might be looking for is "soak up".
Generally I think this would only ever be used metaphorically so it might be worth clarifying:
I will leave her alone for now so that she can soak up the information.
Do let me know if that's not the what you were looking for!
You beat someone up.
You beat someone up badly.
You would not say to someone: Get out of here, or you will get beaten (up) badly [by me].
You would say: Get out of here, or I will beat you up!
That is what you tell someone else: He got badly beaten (up) by those guys.
Figured out means "understood" or "solved", as you noted. I think the problem here is with "it" or "it all".
"He's got it all figured out" would, in general, means "he's got life solved" and would imply that the person has worked out a successful way of living. In this context, it would go beyond merely making a lot of money (because that was explicitly ...