i just got kirin and managed to get her to 35 but another player got ifrit and got it to 100 in less than a hour, what is the best way to level up a special partner or kirin to be specific?

They are leveled differently.
i. Special partner characters gain levels by feeding them weapons, konpeito sweets, or same scrolls.
ii. Mounts gain levels from the your shared character's exp (same goes for youkai partner).
iii. Assist partners gain levels by feeding them warding dungeons' exp tickets/gargoyle tickets.

High leveled players with 300% exp boost running high level dungeons killing golden darumas will get Mount level up pretty quick.
For SP partners if you have a big stock of weapons corresponding with the partner type, and several of the same scrolls, you can max them in a matter of minutes (e.g give Izuna wands, give Gennai axes).
For Assist partners, if you have a stock of exp tickets III, you'll be able to level them up very quickly too.

I forgot, also that mounts and youkai partners can be linked to your character's Exp. But you have to pay 4oc for an hour of that.