The rules say that you "have to complete every required objective." Does this mean you have to reach the target amount (10k for Castle Trodain), or is merely placing high enough to complete the board okay? (2nd in Mt. Magmageddon, for example.)

Merely placing high enough to complete the board is okay, yes.

Usually for individual boards, if you want a decently fast enough time you need to be in 1st place by a large margin anyways. But during Tour runs, our ruleset respecting what the game considers as "winning" could end up saving your run.

Okay, thanks!