Tools
Spyglass+. - Use the spyglass+ to see stats and mutation counts.
When looking at a creature, you'll see each stat with 3 sets of numbers after. "Health 10 / 6 / 52"

• The first number is the base stat. For this example, the creature has 10 points in base health.
• The second number is the mutation counter. Each mutation your babies receive will show up in this location. For this example, the baby has 6 additional HP points added to their base health.
• The third number is the levels that have been added after the creature was raised or tamed. For this example, the creature has 52 added points to health, giving it a total of 68 total points in health.

CMT (Creature Management tool) - Use the CMT to claim, and cull your creatures.
The CMT tool enables players to cull (kill), enable mating, follow, cryopod, claim/unclaim, rename, wander toggle, copy settings, and spay/neuter tamed creates from a distance. When mass killing unwanted creatures, the CMT does the job quickly.
Use the CMT options in your radial menu to enable options, and set the mode.

Understanding Mutations
Understanding mutations can be a bit technical. You may notice throughout the guide that i stressed the importance of having zero mutations in your base breeding line. This is because the mutation counter does not directly corrolate with the amount of mutations a specific baby has. In fact, a babies mutation counter will ALWAYS be the total of the parental mutation counters, but not the mutation points. Often babies will have a high mutation count with zero mutation points in any stat.
It gets even worse if your base breeders have mutation counts, regardless of the points. If a female has any counts in mutations, the baby will get the same count, but not always the stats.
So, if a female has 4/20 mutations, the baby will ALWAYS come out with 4/20, even though they dont have any of the mutations. This is a breeding line ruiner.
You have a 7% chance of a random mutation in any stat if the total combined mutation counter of the parents is 10/20 or lower. If babies are at 11/20 or higher, the chances go down to 4.5%
If you're above 20/20, then the chances go down to 2%.
Start by selecting the stat you plan on breeding for mutations. Typically you want to choose 1 stat as the chances of you getting that specific mutation is considerably low. Adding a second or third cuts the chances of the offspring having the desired mutations in half, or even third.
You only have a 55% chance that the males stats pass on to the baby, and a 7% chance for a new mutation. If you do happen to get a new desired mutation, you then have a 55% chance for the other mutation stat to transfer to the baby as well. This cuts the chances of your babies having the desired mutations down considerably.
There's also the possibility of getting the new mutation in the desired stat, but it's an entierely NEW mutation, not combined with the original mutation points you already have. This happens when the mutation comes from the mothers side. She created a new mutation ontop of the base stats she passed along.

Step 1. Finding the best stats
To start, you'll want to find at least 1 creature with the best stats possible.
Each creature has a max level of 224 with perfect tame. This requires taming a wild level 150 creature and obtaining 100% taming effectiveness. There are 6 stats that make up the total level of your creature. Health, Stamina, Oxygen, Food, Weight, and Melee. The total combined points for each stat + 1 equals the total level of your creature.
The average points in each stat for a max tamed creature is 37, however, you'll want at least 45+ in the stat you plan on breeding for mutations. For a wild level 150 creature, the average points in any single stat is 25. So, you'll want at least 30 points in a wild stat you plan on breeding for mutations.

Step 2. Combining Stats.
When combining stats, you'll need at least 1 creature with the stats you plan on breeding up, and another of the opposite gender to start the breeding process. (A good level'd mate isn't required, so find anything that can get you breeding)
I personally have started with 3 creatures to combine, as each creature had an excellent stat i wanted in my breeding line.
To begin, use a spyglass and compare your breeding creatures. Write down the best stat for each dino as that will be the base stat of your breeding line.
Start breeding your creatures. You do not want any mutations during this period, so throw out any that have mutations. They come quickly in the beginning, so don't worry about throwing away any early mutations.
Keep breeding your creatures together until you have a male and female with the same max stat. You can swap out the male and female with the babies that have some of the desired stats to narrow down the chances of babies getting the incorrect level and stat. (This part of the breeding process is the hardest in my opinion. There's a lot to pay attention to, and it can be difficult to get a breeding pair of the same level and stats)
Again, make sure you dont have any mutations on either the male or female during this step. It will ruin your entire breeding line, and you'll need to start over.

Step 3. Naming Convention.
Naming your breeding line helps with organization and understanding your babies.
I use a method that designates the creature as a breeder "B", the an identifier that separates each creature from other, the gender "M" or "F", and the mutation count. I also add the male parents level to the name as it helps understanding if you have a new mutation or a different mutation. You can also had the stat name you're working on, "HP", "Mel", "W" etc.
Parents should start at M0 and F0 meaning male 0 mutations, and female 0 mutations.
Example "B-REX-M21-288", which is a Breeder, Rex, Male, 21 mutations, and level 288.

Step 4. Build your Breeding Pen
Create a section, building, or tower that's designated for breeding. You'll want this to be a permanant spot as you wont want to move anything once you get started.
For the fastest results, create a location that has as many females within mating distance of a single male as possible. For larger creatyures such as rexes,, i create a large circle of females all with their tails pointing towards the center of the circle, and the male placed in the center. Smaller creatures can be lined up near eachother with multiple floors/layers around the male.

Step 5. Creating your breeders.
By now, you should have a mated pair of identical creatures with your desired stats, set names for your breeding line, and a designated spot for them.
You'll now want to start filling the breeding pen. Start by placing your mated pair in the breeding pen. Enable mating, and start by keeping all females with 0 stats. As you gain females, give them their breeder name, and place them in the breeding pen you've created for them. Don't forget to set the new females to mating as well to speed up this step. Keep breeding until you have all of your female spots filled.
Set aside any mutations you get for later. You don't want to breed out any mutations until you have all the breeder females you need.

Step 6. Breeding for mutations.
Once you hve your breeders going, start hatching. Breeding egg layers is MUCH easider then that of gestation creatures.
For egg layers, get an oviraptor and place it near your breeders. Set it to pick-up fertilized eggs, and wait.
For gestation creatures, youll want to utilize the "Copy settings to neaby creatures" option in the creature radial menu. Disable mating on all breeders until you're ready to start a mating period. Enable mating on your male, copy settings to all nearby creates, wait, and go claim as the babies are born. It's slow, but can be done.
At this point, it gets easy. Pay attention to levels and colors. Babies with mutations will be higher level then your base creatures, and typically come with a new color in a random region. (Note: Not all mutation colors can be seen. Some creatures have empty color regions, and sometimes the mutated color is assigned to the empty color region.)
If you get a male with the desired mutations, immedietely disable the original male breeder so you dont gain eggs you no longer need. This also allows your females to cool down and be ready for the new mutated breeder. Once the male is an adult, set it in the the breeding pen and start step 6 again.
If you get a female with the desired mutation, place her next to the original male breeder with 0 mutations. Breed those two together until you get a male with the desired mutations. Then, use that new male as your new main male breeder until you get a new male.

Step 7. Stacking Mutations.
Stacking mutations is an end game option. You'll want to save this part for when you've succesfully gained all the mutations in two or more stats.
You can go past 20/20 on the mutation count. However, you'll need at least one of the parents to be at 19/20 mutations or lower for the two different stat mutations to stack to the same baby. This is a slow process as there's only a 5% chance the baby will get all desired stats.

(I'll add images and get this updated as i go)