So I kinda want to run the termina map, which btw is incorrectly named on the lbs here (should be "Termina" not majora's mask). But anyway I was kind of confused on the rules. Can the run be done even if the adventure map is complete or is a clean save with an uncompleted map needed?

This is based off NG+, so this is assuming you have beat the map prior. Keep in mind that the current rules are based off what one runner did in HWU so they could be changed/new category made.

TLDR; Yes you can do the run if you have beaten the map prior and it is recommended you do so.