As a tame Monster continues to live with you, his/her Levels will increase. Originally, I thought that their levels increased with time but now I believe that they increase according to the amount of experience they gain.
A Silver Wolf when first tamed has an HP level of 65. My Silver Wolf now has an HP of 186. Yesterday, his HP was 180. this morning, when I took him with me into a Cave, he was fighting a Monster when I received a prompt to the effect that a 'Level increased.' MY level did not increase. In fact, I was walking towards a Generator at the time, and was involved in no other activity. It was the Silver Wolf's level that increased, adding 6 points of HP to his total.
I need to confirm this, but it appears to me now that you need to use the Monster actively in order to increase his/her levels. In terms of a 'farmhand' Monster, I imagine that levels would increase with farm labour. In terms of Monsters that give Ranch products, levels should increase according to the number of times that you have obtained product from them. It is not combat alone that raises levels but use, I believe. It cannot be Heart Level that determines total HP as all the Monsters I have are at 10 Hearts and have been at 10 Hearts for a couple of seasons. Nonetheless, their HP continues to increase.
I would be interested in confirmation by other players as to the speed and amount by which their tame Monsters' HP increases. Unfortunately, you cannot see your Monsters' actual Skill or Experience levels but only their total HP and Heart Levels.
You can see any tame Monster's HP when you access the board in front of the Barn that displays the status of all the Monsters in the barn as well as total Feed, Friendship Levels, Ranch Products to be obtained and any farm tasks that a Monster can perform. When you tap on an individual Monster, its description and total HP will appear on the top screen.
My Orc currently is at a total of 170 HP. If I send him to the Forest of Beginnings and tame a new Orc, his total HP will be 45. All of my Buffamoos are at a total of 205 HP. If I send one back to the Forest of Beginnings and tame another, her total HP will be only 80.
I would have thought that total HP increased according to the length of time that one had the Monster, but when my Silver Wolf's HP was the only one to increase and it occurred when his level increased during HIS combat with an enemy, I realised that it must be a situation where each Monster's HP increases individually. The only way to disprove this would be NOT to use a Monster at all for a couple of seasons and see if his/her total HP nonetheless continues to increase...
By the way, the Silver Wolf is the only Monster I use in combat situations. The Orc is used to harvest Crops, my Goblin Pirate waters crops and the other Monsters in the Barn produce Ranch Products. All have increased in total HP over the course of time. I expect therefore that obtaining Ranch Product would increase those Monsters' levels and performing farm tasks would increase the farmhand Monsters levels.