I don't think Intrigue is appropriate - I do think Int + Order of Hermes Lore + Reputation of 9 or more would do it for me, provided the archmage has faced at least one challenger. There's not way to know if they have never faced anyone.
As you may have already understood, in my game, an archmage challenge will be highly advertise all around the tribunal and even in other tribunals.
Of course, sometimes a challenge can be discreet if it involve something special (like a long lab research, findind a unique book, negociation with a faiery lord). But, considering the importance of the status within OoH society, the fact that at leat 3 tokens from other masters are needed to pass from journeyman to master (see Guardians of the forest p.22 to 24), i think that becoming an archmagus is an hermetic society event in itself. Consider the type of feat or service a magus must realize to become one(it can have impact on the whole). In my saga, i intent to use an archmagus challenge to resolve an old problem/mystery in the tribunal that, once resolve, will have impact on the whole tribunal.
I even consider that the deed is sometime used in presentation of the mage... See, it's X archmagus, from Y house, filia of Z that is the (insert the feat here; slaye of this, friend of that, inventor, you name it)
I can see both arguments.
All, thanks much for all the help. It is very much appreciated.
It looks like this topic has run it's course. Again, thanks for the advice.