I think that you should start with basic mechanics of the magic in your world. By defining the mechanisms behind the magic and the rules that govern it you will be able to adjust difficulty levels and create suitable obstacles in achieving a status of an Archmage.
I think these are the questions worth asking:
1. What is magic? (form)
This is a fundamental question. Is it akin to matter? Or rather a force like gravity or electromagnetic force? Does one need a physical contact or a physical manipulation (besides vocalising) to be able to use magic?
So, if magic is a type of matter, you can simply limit its quantity. Those who can collect more magic (mana :) ) are capable of greater spells. If magic is a force then you can think of a type of force and different problems associated with their practical use.
These, of course, are not the only possibilities. Just some examples.
2. The source of magic
Basically, it is where the magic comes from. Does it have a particular source? For example, magic is generated by a mage. Then, the more magic a mage can generate the more powerful they are. Magic output can depend on food, meditation, DNA, and so on.
Maybe the source of magic is established by some higher beings, i.e. divine magic. In this case, the limitations can be associated with either the establishers themselves (a mage has to have a good relationship with the higher power in order to perform spells) or the access to the Source (higher beings have used a complicated language and the Source responds only to it; the Source can be accessed only in a particular mind state; etc.).
Your world might not have a single source of magic, which then will be somehow dispersed. However, this dispersion can be uniform (and here we have a problem of concentrating the magic to drive a spell) or not (something like the places of concentration of power, power lines, etc.; hence the problem would revolve around a distance from those places or lines of power).
3. Nature vs nurture
Who is capable of learning and performing magic? Does one have to have some innate ability or blood and sweat can get them there?
If you resort to nature, you can easily control the number of mages by manipulating a distribution of right genes in your population. You can also limit magic abilities to certain blood lines or birth conditions.
If you decide that everyone willing to learn can become a mage, you can adjust the learning curve to make it easier or harder to obtain power. You can also play with the availability of this knowledge. Some families can have heavily guarded spellbooks that only the older sons or daughters can access. Your heroes can be on a quest for some lost books.
4. The usage mechanics
How exactly the spell works?
Does a mage channel the magic through their body (stamina, physical endurance, pain tolerance, etc. can come into play) or their mind (important factors here would be willpower, attention spans, logical abilities, intelligence, self-control, mental stability, etc.)? In this case, a mage functions as a conduit. They can be damaged by tapping into too much magic. They can burn out. They might risk their physical and emotional integrity every time they perform a spell.
Another possibility is a mage as a catalyst. It can be an interesting scenario since it allows for some fun limitations. For example, aptitude for magic can function as catalyst quantity — the higher the aptitude the faster and stronger spells can be performed. Since catalysts only speed up and facilitate natural reactions the spells can be limited to natural for your universe processes and changes. E.g. magic can cure cancer (because it is a natural process) but it cannot regenerate amputated arm (because humans do not regenerate limbs).
The next approach is to use a spell (or a ritual associated with it) to focus magic. In this case, you can play with the difficulty of rituals and levels of precision required for a spell to produce a desired effect.
A spell can also be an activation mechanism, i.e. all the magic needed is already there, but one needs a correct trigger to start a chain reaction. A mage would have to know what triggers what, what is the critical point, and how to contain the spell. The idea of the chain reaction opens enormous plot possibilities. Things can easily go off the rails. There is always a chance of unexpected consequences due to mutations during the chain reaction.
What is the true significance of the rituals?
For example, in case of incantation-based magic do the words truly matter? Can it be that the spells consisting of words are just a vehicle for creating a certain melody or a certain consequence of sounds? How important is understanding of a language used for spells? Can someone just learn by heart the pronunciation of a spell without understanding the meaning?
Are the rituals set in stone or they are more flexible. It makes for a very different dynamics if a mage can improvise on a spot.
6. Spell "aftermath"
What happens to magic after a spell? Does it dissipate? Can it be infused into a material object? Does the law of conservation of energy apply to magic?
What if magic charges an object of a spell? Then depending on magic mechanics, future spells can be easier or harder to perform. Mages can keep those objects due to advantages they have. Alternatively, mages have to be very selective about magic applications because they might not be able to affect an object again.
If an object can be given magical qualities what kind of qualities those are? And who can take advantage of that object? Can mages mage items for non-mages? Or all magic is limited only to people with corresponding abilities?
This is not a straightforward answer to your question, but I still hope it is helpful.