To get the Archmage achievement, you must need to obtain EIGHT different Wizard endings.
You can and have to make use of the save function, so that you can reload in order not to go through the whole visual novel. Or else, you can decide to do eight different playthroughs! :)
I'll list some choices that work, but since this game is based on a charisma/strength/intelligence system other choices would still work great. This isn't the shortest route, it's a route which will give you the achievement :)
I'll also try to list where you can save and reload in order to maintain the previous choices and obtain another Wizard ending.

I
Use computer.

II
Go to the bathroom. (str 1)
Eggs, bacon and ham. (str 2)
No.
SAVE #1
Lean in a bit closer.

III
RELOAD #1
Ask her what her major is
SAVE #1
Sit closer to the front next time to get a better look.

IV
Go to the bathroom.
Oatmeal with lots of blueberries.
Yes.
Ask her what her major is.
Check the syllabus.
Go look for a club on campus to join.
Avocado toast.
Fine I'll do it.
Tell her off.

V
RELOAD #1
Check the syllabus.
Go home and study. (int 2, str 2)
Avocado toast. (int 3, str 2)
Fine I'll do it.
So what are you doing here?
Go home and study (int 5, str 2)
I'd like to be your friend too.
Yes.
SAVE #2
It's none of your business. Better go pick up Ellie before she gets upset.
That was a long time ago! He has probably forgotten all about it.
Sure.
Strike up intelligent conversation.
Any plans for the weekend?
Play tennis.

VI
RELOAD #2
Save Lia.
Don't you remember what I've said before? I'll always be there for you.
I didn't do anything.
SAVE #3
Run for it.

VII
RELOAD #3
Fight.

VIII
RELOAD #2
I don't want to.
Compliment her body.

Hope everything is ok, I'll recheck too sometimes :)

If you get lost somewhere, here's the link of the awesome HTML comprehensive guide with all the answers written by TheMightyRoast/Tim Roast, even though since that guide was made for the XBox, it didn't comprehend the achievement we wanna get :)
https://www.gamefaqs.com/xbox360/657780-dont-die-dateless-dummy/faqs/65742