Praise and punish
In Monster Rancher the player will have the option to praise a monster when it does something right and to punish a monster when it does something wrong. If the player always praises the monster for doing well and never punishes the monster for doing poorly then the Monster will live a long and healthy life. The downside is that the monster will be soft in battle because it has never been punished. If a monster is always punished for doing poorly and never praised for doing well then it will become angry or sad and stop listening to instructions and possibly even run away or die young. A good balance of praising the monster when it does well and punishing the monster when it fails will make the monster live a healthy life and also be tough enough for battle.
Food
Check the monster's bio to see what foods the monster likes and dislikes. Only buy the monster's favorite food when it has accomplished something big. Don't give the monster its favorite food just for accomplishing a menial skill but for performing well at a tournament. The rest of the time feed the monster healthy foods like vegetables and vitamins.
Exploration
Sometimes an archaeologist will come to the ranch and ask for the monster rancher and his monster to assist him on an exploration. Any items that are found the monster rancher can keep, so an exploration can be beneficial. Don't use the same monster for more than two explorations because after that, the chances of the monster getting lost are very high and when a monster gets lost the monster rancher will lose him for several weeks and that is less time the monster has to be trained.