Have someone else do it?
Unfortunately, once cast aluminum is pitted (can't tell from pics) it's usually beyond bringing back to "new."
If it's pitted bad enough, I sometimes Bondo and then automotive paint a complementary color (rather than try and make it look shiny).
Powder coating is also sometimes an option, depending on surface condition.
If it's not too far gone and you're willing to put in the time and effort to make it shiny, it's a matter of doing it like the skins with varying grades of sandpaper and polishing compound, but it's way more difficult when you're trying to get into nooks and crannies.