I really want to hold some sort of PVE event but I can't come up with a way to make it a competition. Suggestion?

If you really want to do a PvE event, and you want to make it to feel like some sort of a competition, it maybe is an idea to make it like a speedrun, or who defeated a specific boss quicker than the other group. and do you wanna do a instance or a dungeon event? you can also do that the team who has completed 5 dungeons the quickest has won, all sort of things that is possible to do :-)