There are 21 elemental challenges so far (22 if they create an Electric-Dark combo). Since some animals will present the maximum possible NEB against more than one type, it should be possible to cover all types with 5-10 animals as Anyuszko suggests.
MINIMAL SIX
Based on my insane fight charts, Emerald, Terradactyl, Nightmare, Griffin & Sloth present the best odds against 19 of the 21 current types. The two types they don't trump can be met with Magmacore and a super Electric other than Terradactyl. So all bases can be covered by a minimum of 6 animals.
(Substitute Ox or Phoenix for Nightmare. Substitute Grassquatch for Sloth)
If you don't have an Emerald, Pegasus scores the same NEB against Earth and Earth-Nature, which are the only opponent types to which I've assigned Emerald. If (like me) you don't have all of the 5 supers I've mentioned, you can certainly use other supers, but you will then have a larger group of champions. This can of course be a good thing, but involves a greater investment of food. You may also need a couple rares to substitute if you're missing key supers like me. Beagle & Daredevil have to be in my fight club since they're my only Electric rares and I have no Electric supers.
HIGH ROLLERS
As you raise your tournament cohort, keep in mind that the highest NEB any animal can score against another is 2. It won't happen for most matchups, but the following supers deliver:
Terradactyl against Electric-Water & Electric-Fire
Lion against Dark-Nature
Phoenix/Ox/Nightmare against Gem-Nature & Dark-Nature
Griffin against Dark-Fire, Earth-Fire & Fire
Grassquatch/Sloth against Electric-Earth
Magmacore against Electric-Dark, Electric-Fire & Dark-Fire
Vinotaur against Dark-Nature.
The following is a REVISED list of MVPs overall (not all among my own animals) in descending order:
A. Lion, Magmacore,
B. Phoenix, Ox, Nightmare, Vinotaur
C. Terradactyl, Pegasus, Sloth, Grassquatch
Each of these MVPs is the best pick against 5 or more elemental types.
Keep in mind that top performers may overlap each other so you don't need them all. Although Lion scores the highest NEB against 7 elemental types, Phoenix & Terradactyl cover 5 of those 7, and you may have animals that cover the other 2.
As for whether any of the animals I've mentioned actually NEED to be L15, I find L10 to be sufficient in most cases but, if you can spare the fruit, L15 could certainly add to your advantage.