Resetting Pets:

There are a number of ways to reset pets On this page we will talk about them.
Pet Reset using:

Pet Reset Cost

Pet Shops are located in any Major City (Ex: Goldburg, Bagdad, Emerald...). This is the equation to calculate the cost to reset a pet at the store, it would also be the same cost as using a downgrade.
Price Range
01-10 500 X level of pet + 2000 2500-7000
11-20 1000 X level of pet + 2000 13000-22000
21-30 1500 X level of pet + 2000 33500-47000
31-40 2000 X level of pet + 2000 64000-82000
41-50 2500 X level of pet + 2000 104500-127000
51-60 3000 X level of pet + 2000 155000-182000
61-70 3500 X level of pet + 2000 215500-247000
You can follow the pattern to calculate any level pet. The equation to calculate attribute outcome this manner is:
|PetStatus / 20| + 2.

Pet Shop Fusing

You can also reset a pet back to level 1 by fusing two of the same pets together. If you fuse two different pets the outcome can be random, but if you fuse the same pets together, the outcome will always be that pet at level 1. Fusing pets only costs 5k coins, no matter what level. The equation for the level 1 attributes of the pet after fusing is:
|Pet1Status / 20| + |Pet2Status / 20| + 2.
Step 1: Have two pets non ensnared and preferably at the highest level you can get them (for highest lvl1 status).
Step 2: Go to a Pet Shop and speak to the NPC that performs the fusion.
Step 3: Choose Please Fuse My Pet.
Step 4: Confirm the 5k fee for fusing.
Step 5: (For this type of merge it does not matter the Parental or Maternal pet, however later on if you are trying to get different types of pet species from merging like creating a dark str/str pet, you will have to make a choice here, for now it doesn't matter.)
Choose Paternal Pet (Example: Faya Elephant #1)
Step 6: Choose Maternal Pet (Example: Faya Elephant #2)
Step 7: Choose the bottom option Not Necessary, just fuse them.
Congratulations! After confirming the fuse you should have a level 1 of whatever pet you fused (in our example a Faya Elephant) with better starting attributes then a regular reset. This is the preferred method for fusing. Assuming we can afford catching two of the same pet you want to fuse and paying the 5k, otherwise The following option is available.

Pet Collecting Book ( Free Reset)

To perform this fuse you only need one ensnared pet. It is free to perform but the pet will not gain any bonus attributes.
Step 1 You must have a pet that is higher then Level 1 (Capped still)
Step 2 Click the book in the upper Right hand corner
Step 3 Choose the Pet Book (icon to the right of this line)
Step 4 Click the Arrow button (Release the pet)
Step 5 The warning appears telling you the pet's ability, color, HP's, skills will be reset to 1 (Choose OK)
Step 6 drag the caught pet into the box on the right and hit O to confirm a notice will say "Pet saved succesfuly"
Step 7 Click the Pet Book again
Step 8 Click the Sort button and the pet will move to the top of the list
Step 9 Click on the pet's name and click the button marked "Take Out" Click OK and your pet is now level 1
The logistics to doing this method if you cannot afford to merge a pet in any other way. This will not give you any bonus attributes at level 1, all status will be 2.
Thank you eXimus for the guide and Hellkitten for the (sort tip)

Reset Using Downgrade Formula
Pet Level-down Property

You can also reset a pet utilizing downgrade formulas to gain more initial attributes. This is available at the same NPC that performs a regular reset. You also need to pick a gem that will give you an extra boost to whatever status it matches up with.
To do this kind of merge you need: a non ensnared pet, the pet downgrade formula you wish to use, a gem of your choice and the money to cover the cost of reset.
Here is the list of the gems you can use:
Green Jade = CON
Mythst = INT
Red Jade = STR
Yellow Jade = Luck
Blue jade = Dex
Azure Jade = Cha

You can only use ONE gem and ONE downgrade formula per each reset
Bellow are the equation for the outcome attributes:

Milk Reset Equation:

Enhanced by gem: |lvl/10| + |stats/10| + 4
Other Attributes: |lvl/20| + |stats/20| + 8
Juice Reset Equation:

Enhanced by gem: |lvl/8| + |stats/8| + 6
Other Attributes: |lvl/20| + |stats/20| + 12
Coffee Reset Equation:

Enhanced by gem: |lvl/6| + |stats/6| + 8
Other Attributes: |lvl/20| + |stats/20| + 16
Soda Reset Equation:

Enhanced by gem: |lvl/5| + |stats/5| + 10
Other Attributes: |lvl/20| + |stats/20| + 20
Cola Reset Equation:

Enhanced by gem: |lvl/4| + |stats/4| + 12
Other Attributes: |lvl/20| + |stats/20| + 24

Credits to: ICatchPets, Moiraine & MeFisher