Breeding monsters is the key to beating this game; the game will get exceedingly difficult after certain points if you do not consider taking time to breed stronger, more versatile monsters every now and then.
While you can breed monsters once they reach level 10, it is best to breed them once they reach at least Lv20, this will ensure that the offspring will have better stats than its parents. The higher the level, the better.
Listen well to what people say as you might gather important information.
Record your journey frequently. You need the BookMark to record the journey in the Mystic World dungeons.
Sell or store extra items as you can only carry 20 items. You can store them at the Vault.
Get new magic skills and special skills through breeding and matching. New monsters can acquire new skills that their parents don't have.
If you are breeding solely to pass on skills, then it is not really necessary to level a monster to 20 if you don't wish to. However, If the skill(s) in question are not skills learned naturally by either parent monster, then it is important that at least one parent currently knows it before being bred. Additionally, it is important that the monsters actually have the stat growth needed to learn the skill(s) before they reach their level cap.
Get new abilities through breeding. When an ability you want is not in your monster's nature, it can be inherited from other monsters through breeding. Try creative ideas to breed and raise your own powerful, original monsters.
Wildness increases at Monster Farm. When you leave monsters at the Monster Farm for long periods of time, their Wildness (WLD) value increases and they will start disobeying during battles. The monsters you're interested in raising and making powerful should be taken with you on your journey all the time.
If you have a monster you're interested in training but do not wish to take it with you right now, you should put it into Sleep mode so that its WLD stat does not ever increase. Keep in mind that said monster will receive NO experience points while its hibernating.
Add Speed to healing and recovery skills. If you have monsters with high healing or recovery skills, be sure to increase their agility with items like AGLseed. This will allow your party to heal or recover first during battles, before enemy monsters renew their attack.
Selling items is the only real way to make gold in this game. The best way to make gold is to collect the various Staves (LavaStaff, WindStaff, etc.) while exploring dungeons and sell them to the Merchants randomly found in dungeons for the full value. This is a common practice among players since having good monsters will negate the uses the various staves would have had in the first place. The Warpstaff should not be sold though, as it's effect is always useful and does not have a monster-equivalent ability.