How to Level Up Palico and Palamute Buddies
Clear Quests
Palico and Palamute buddies will earn experience points if you take them with you during quests. The higher the difficulty of the quest, the more experience points they will gain.
Use Dumplings for Buddy Leveling
Eating the Anko Otomochi dumpling grants your buddy increased experience gain during the quest. Be sure to take advantage of its effects if you want to level up your Palico and Palamute fast.
Training at the Buddy Dojo
Palico and Palamute buddies can earn experience points outside of quests when you enlist in the Buddy Dojo. You can register up to 6 buddies at the dojo and they will gain experience points each time you have cleared a quest.
Akin Acorns can also be used to further increase the experience your buddies obtain while training at the dojo.
Meowceneries
Your buddies will also earn experience points when you send them off on Meowceneries expeditions. Note that they experience they will gain will be lower than if you take them on quests or enlist them in the dojo so this method is not recommended for fast leveling.
Tips for Leveling Buddies Fast
You can bring up to two buddies on a quest when playing offline which is good for fast leveling. Your other buddies should then be enlisted in the Buddy Dojo as often as possible.
If you simply want to focus on leveling buddies at the dojo, just do any quest that you can clear within a few minutes. On average, your buddies will go from level 1 to 10 in about 20 minutes.
Which Buddy Should I Focus On?
Since each buddy in MH Rise can have different sets of skills, it is recommended to reroll them at the Buddy Scout facility. This is to allow you to select a buddy with abilities that synergize well with your playstyle.
What does leveling the palico/palamute do? Increase their damage, life, etc.?
This was my question too.