Alright, so I was going through the Mage Quild quests as usual. First, I completed all of Ajira's in Balmora. I then went over to Edwinna in Ald Rhun, I completed her quests until she told me I should speak with Trebonius.

I went to talk to Trebonius and he wanted to have a showdown in the arena, I agreed. When I killed him, it said in my journal that I had become Arch-Mage, but it didn't say that in the Mages Guild status in the menu, it still says "Master Wizard"!

I figured I should ask about advancement, Ajira and Edwinna won't do anything, so I went over to Skink in Sadrith Mora. I did all of his quests (still not getting advanced to Arch-Mage) until he gave me the letter for Trebonius. I can't give this letter to him cause he's dead!

There aren't any more missions and none of the stewards will advance me to Arch-Mage.

My question is: What do I have to do to get my status in the menu to change over to Arch-Mage?

(it only said In my journal I had become Arch-Mage, everyone still calls me Master Wizard)

you can't, this happens because you didn't make sure you had full advancement by asking, I did this the first time I played but the second time I talked to Edwinna before killing Trebonius, she told me I was master wizard then I killed Trebonius and became arch-mage

the only way you will be able to get status of arch-mage now is to reload a previous game and talk to Edwinna or Trebonius about advancement first

I forgot to mention that, the last advancement I got from Edwinna was Master Wizard.

I killed Trebonius when he wanted to fight, and I'm still Master Wizard.

Did you talk to Ranis Athrys in Balmora? She is the Guild Steward in Balmora and also gives quests. Also, is one of your Favored Skills at 90 or more? The Favored Skills for the Mages Guild are Alchemy, Mysticism, Illusion, Alteration, Destruction, and Enchant. I think you need one of these at 90 or more and two others at 35 or more to be officially named Arch-Mage (plus a minimum Intelligence and Willpower of 35). If you don't have the necessary skill levels, train them up and then ask again about Advancement.