Also, knowing the missions ahead of time would be useful.

So a tower has 15 floors and you get two attempts per day, as I understand it. It's an 8 day event, so the intention is that those who want to perfect the given tower event need to succeed on every attempt (15th floor asks for 2 clears). Each floor gets 3 missions.

1st mission is 'clear it once' for floors 1-14. As mentioned, floor 15 asks for 2 clears.
3rd mission is 'clear it using only this specific element'
2nd mission varies between 'clear with 3 survivors', 'clear with 5 survivors', and 'clear with 2 of this type of kamihime' for floors 1-14. Floor 15 asks for clear within 15 turns. So it's possible to accidentally lock yourself out of being able to deploy the specific requested type.

Also, this is actually a competition. Ranking is determined by the number of tower medals acquired, with the prize being more tower medals. To that end, there are small amounts of medals given based on how many turns you took to clear a floor; they're functionally tiebreakers in the end.