In this category : https://www.speedrun.com/rblx_entrypoint/full_game#Planned_The_Final_Strike
(https://prnt.sc/say20c)
I did a duo run and a solo run, but I don't want my solo run to be obsolete, I've tried every "player obsoletion mode" options, and it's the same everytime.  My partener's solo run isn't obsolete tho, it's only obsolete for player 1.
Can anyone help me ? x)

I think the solution is to split the categories (or add a new sub-category) to "single player" and "multi player" runs. 
Take a look at any LEGO game (for example https://www.speedrun.com/lswtcs ), they have a sub-category of "solo" and "co-op" for any one of the main categories.
Not only it will solve the obsolete issue, I would imagine a co-op run to be always better than a solo run in most cases, so they aren't comparable by themselves, and maybe shouldn't exist in the same leaderboard.