Follow these steps to get your first puppet + last "Cat Butler Ariel" quests:
1. Take quest from NPC called Ariel at Supply Depot in Jackson Adventurer Association named "Cat Butler Ariel I" and follow the quest's steps. Go to Hunter's Hill nearby Sanctuary and use drowsing (USE SPACEBAR) to search around for a cat mentioned in quest, after this come back with it to the location where you took the quest from.
NOTE: Make sure to not run too quickly because the cat that follows you can lose it's way and you would need to go find it at the same spot you have found it at while using drowsing again! And remember to have at least some spots free in your inventory before you begin all of these quests!
2. After finishing quest "Cat Butler Ariel I", new quest will appear called "Cat Butler Ariel II", read what it requires you to do then complete it and after this quest another will appear named "Cat Butler Ariel III", complete it as well like you have done with "Cat Butler Ariel II".
3. Once you complete all 3 quests, you will get your first puppet which you can find at tab Character-->Puppet or press button "N" to open Puppet panel directly. And don't forget to accept all quests that will be given to you after "Cat Butler Ariel III" and they are named as following:
a) "Cat Butler Ariel IV"
b) "I am a puppet tamer!", "I am a puppet sitter!", "I am a puppet master!"
These 3 quests mentioned above are necessary to be finished first to complete quest named "Cat Butler Ariel IV". It will take you time to complete them all so always make sure to come back to NPC Ariel at Supply Depot in Jackson Adventurer Association whenever you can to see if one of your quests were completed.
NOTE: Don't trash these quests from your questlist, they can be retaken from NPC Ariel but keep them in your list so all actions you will apply to your puppets will make these quests finished.