Taming a beast to mount

Since the community of WLO developed, it become a competition to have better team. Even though you become 190rb lv which is highest level of the WLO that can be achieved, or on other hand 650stat point became a limitation to you, you need someting else to improve your stats. Having a good set of items will boost your stat too. Morover having a good ride will significantly increase your stats as well.

You will be able to gain some percentage of the stat of your ride.
Bash Saddle -> +1/3 ATK
Magic Saddle -> +1/3 MATK
Swift Saddle -> +1/3 SPD
Defence Saddle -> +1/5 DEF
Spirit Saddle -> +1/5 MDEF
Decelerate Saddle -> -[200-(PET AGI*2)]

Well it's straight forward, if you want to decrease your spd amount use lowest agi animal pet. If you like to get SPD make sure your ride's element is wind. If you like to have ATK or MATK go with the fire type mountable monsters. In short to maximise your gain you should choose your mount wisely.

->First thing to know is that you'll be able to change your pet's stats at 20th lvl earliest. It'll cost less washing(will explain it later) cycle to achieve what we are going for.

->There will be some amity drop on pet(-10 is the min penatly for trade) when you trade it and the max amount of amity that pet can have is 50 when trading it. So no point of having higher of it. But beware you shouln't use your pet on fights below 25 amity it may runaway(leave your team). We'll be gathering stars to trade this stars for amity on Welling Village's flower girl Yuna to cover up those amity drops.

->Observing the pet's own build on it's stats and deciding to when to stop training to wash it or keep training.

I'm pretty sure everyone has their fancy cool pets to ride it, but i'll be only focusing those can be catchable by players.
Green leopard is good to use for SPD purpose since it's wind element and good base stats.

Deadly Flower is good to use for MATK or ATK purpose. It's burstable pet with assist skill which makes it to easy to get highest lvl. Recommended type is fire since it's atk increased higher by it's lvl. Note: Wind Flower doesn't have assist skill to be able to burst it.

Place to catch Deadly Flowers
credit goes to Naru from wlodb
There are more creatures to use but those one i have been using myself. If you are looking for more go ahead to guide of Metatron's on wlodb

1- Create 3-4 characters and burst them till Lv40+(suggested for flower, other pets may need different levels).
2- Do pet return sc quests and star quests on those characters that you are able to or willing to .
3- Exchange stars to amity flowers on welling village by Yuna.(Talk with elliot to finish quest related to yuna then you will be able to exchange stars to amity flowers)
(have atleast like 7 amity flower. 1*star=6*Amity) (You will get 2*5Amity while doing Pet Return Scroll quests. Total of 50+ amity is enough)
this is what basically you'll have when you finish quests i have mentioned. 
4- Keep trading your ride pet through your characters to swap stats to wished one and increase their amities before trading.
5- This step is extra but you might try Pet EXP Boluses Quests as well to reach higher lvls like 199.

Big thanks to darkdeaver on wlodb for that detailed guide about pet Lethe quests.

Neccessary vehicles : Submarine & Air vehicle
Neccessary items     : Ladder, 3*Stuffed Buns
Neccessary pets       : Senior Beetle(M)(23lv one), Rain forest Frog(dark green one), Squirrel (find one near entrance of cirrus farm), Easy-going Buffalo(Water-nearby to chang-an village entrance)

1-Holy-          Use a flying vehicle to open box at holy village's church's backside
2-Holy-          Saar's research, give senior beetle, rain forest frog and squirrel in order.
3-South Pole- Find the other sledge wolf which at left side of town.
4-Korea-        Click the box near waterfall where gs quests fights are.
5-Thailand-    Goto near the Palace, talk to the man and then go inside the palace and click to ox owner.
6-Inca-          Talk to Alien, on leftest animal pattern on map.
7-Athens-       Goto library talk with lady, (dont click twice it gives forgotten scroll instead) Go to the cow you saw when you entered the city keep going till the end of map to left.
8-Fishin V.-     Click frog 10times on left side of the entrance to village by port.
9-Changan-    Talk with Gouzi and bring him easy-going buffalo
10-Changan-  Next to gouzi there is a dog on roof, bring ladder to get it
11-Koyota-     Help Momotaro to find his pets (Chicken,Dog,Monkey). After giving pets to momotaro. Go to Ghost Isle- Bring 3*Stuffed Buns to give Momotaro and fight with Ox-headed demon.
12-Mayan-      Help crew to fight with mayan tribe.(most bottomleft corner of map)
13-Undersea- Use submarine to get rightest side of seabed to talk with turtle(minigame)

Big thanks to Hei on wlodb for that detailed guide about star quests.
I'm chosing the most easy ones which conclude some easy fights or not fights at all.
You should have atleast 7 stars. Choose the quests you want to do from below list.

**Kelan Village
Grandparent and Grandchild Who Are Robbed Star*1 (save xao from pirates)
Pig's Nightmare Star*1 (minigame)
**North Island
Story of the Hood Girl Star*1 (beat wolfs)
The Spirit and the Golden Axe*1 (be honest with fairy, pick iron axe choice)
**South Island(N)
Sheep's Nightmare Star*1 (mini game)
**Holy Village(Main)
Attendant Star*1 (you need to help magellan first to be able to do this quest at holy village pub)
Unbelievers Star*2 (fight with the bishop and others to save indians)
**Holy Village(SW)
Find the courage stone Star*2 (maka cave stone golem fight)
**Holy Village(SE)
Fish Food Star*1 (bring pink earthworm from northisland cave to fisher and dont kil it)
**South Island(S)
The Mark of Going Home Star*1 (Pass the 3rd floor of Maka Cave -Top Left arrow- and fight with parrot to help girl keep her trail)
**Stoowa Isle
Xaolan's Fate Star*2 (poor xao killed by spider)
Protector of the Holy Spirit Star*3 (totem fight,available after xao dead quest)

I'll just leave the link of the whole quest for +20 Spar anyone willing to do.

In my opinion everyone that are able to do such quests and burst thing should create his own epic mount. You have to put some effort but it's reasonable. In the end you will have a pet with high ATK, MATK, SPD which will boost your stats. I may or may not make some mistake or forgot some details. I might explained some of the quests wrong. Feel free to tell me to make my guide even better. %#