"Invent a 7th magnitude spell" isn't a challenge or necessarily a benchmark for one, but a different requirement. Back in AM2, it was much harder to invent that kind of spell. Art scores were generally lower, there were no Magical Foci and the mighty lab bonuses of AM5 were yet to come.
But an archmagus' challenge.... it seems to me that there needs to be some kind of challenge there versus the defending archmagus. It's not about success but victory. So a Merinita whose challenge is to succeed at an impossible story ought to have already succeeded either at that story (preferable) or a similarly impossible story. A Bonisagus who demands a breakthrough ought to be able to point at his own breakthrough and say, "beat this." A Criamon who demands a Shrubbery....
I still stick y all the old benchmarks: a newly invented spell of at least 7th magnitude, trained at least one apprentice, and has done something noteworthy and prestegious. After that though, the challenge can be as easy or difficult as desired. It can be a race, a contest, a breakthrough, a certamen or a comat, or anything the archmagus thinks of. I suppose that there is peer pressure from the other archmagi to prevent ridiculosly impossible challenges, such as trapping God in a box.
In my games, no one has issued an Archmagus challenge in years. But in the past, this is what I have done... Cicero of Bonisagus: Obtain one magical secret from each tribunal that I do not already know Michael Augustus of Flambeau: eliminate a major threat to the Order (he will designate which threat you are to target) Frederique "Fuego" of Flambeau: Bring me the heart of an ancient dragon Cryotaxx of Criamon: Solve the Seven Riddles of (some fancy name that I have long forgotten)
To Ovarwa's point, I can see where you are coming from. By beating the archmage, you are demonstrating that you are as good as at least one of them. A good argument. I'm still stuck on the need for a "wow factor" but perhaps that can be made up in requirement for an Order-wide reputation. Beating an archmagus at his own game does have some wow, but it also seems like one can get very, very, lucky.
Ooo! And boy would the Infernal like someone on the Council of Archmagi. Talk about the temptation to use outside means of passing the challenge!
This actually was tried by yours truly (well, Ardeus ex Jerbiton) in one of ours sagas I had to tell him and I had a year to prepare and a month to do the deed. I failed miserably, but it was good fun, with teleporting grogs jumping all over Europe to locate him and then me trying to trap him so that he couldn't cast Parma Magica and so I could beat him (3rd edition so my penetration was not that amazing compared to his parma of 9). I located him, but didn't count on him being playing chess with a dragon or the fact that one of the effects of his talisman teleported him to safety if he was immobilized or severely wounded. So he escaped me. He ten came back and immobilized me with a Moon duration spell that placed me in stasis in his sanctum, and then proveeded to move in front of me for a month without puting up his parma.
I ended up being offered membership in the Archmage council (no challenge) after recovering a Mercurian ritual and managing to cast it: it made all the major roads of iberia impervious to Djinn activity (ReVi). Took Ardeus 5 years to complete (and A LOT of vis), but it was cool, and made those Flambeaus out there green with jealousy The spell was cast in 1211, if that tells you something
Seems that we had some infuence there.... Quaesitorial investigation declared us innocent of everything. Of course our covenant was razed by a bunch of demons in 1215 in a climatic end of the saga that sent all of us straight to hell, but hey, that is minor side stories.... It might be connected to our past achievements, or it might not.
I had to tell him and I had a year to prepare and a month to do the deed. I failed miserably, but it was good fun, with teleporting grogs jumping all over Europe to locate him and then me trying to trap him so that he couldn't cast Parma Magica and so I could beat him (3rd edition so my penetration was not that amazing compared to his parma of 9). I located him, but didn't count on him being playing chess with a dragon or the fact that one of the effects of his talisman teleported him to safety if he was immobilized or severely wounded. So he escaped me. He ten came back and immobilized me with a Moon duration spell that placed me in stasis in his sanctum, and then proveeded to move in front of me for a month without puting up his parma.
The spell was cast in 1211, if that tells you something 
Quaesitorial investigation declared us innocent of everything. 
Of course our covenant was razed by a bunch of demons in 1215 in a climatic end of the saga that sent all of us straight to hell, but hey, that is minor side stories.... It might be connected to our past achievements, or it might not.