You start off as level 1 and have to fight monsters first to level up. All of the girls are heroines and are actually quite strong. (The lowest level heroine was like level 14 in the demo). Your level doesn't need to be higher than your enemy to defeat them, but obviously the higher the level gap, the more difficult it is. It mostly determines how much damage you deal and receive.
The first set of monsters are I think level 2 through 6. When you select the enemy, their level is the first number displayed. The Slime is the weakest monster level-wise, of course. Remember that you start off with some potions that you can use to heal, and you can buy more from the shop for 30 gold.
After you defeat the first set of monsters, you get a slave girl and maybe a treasure chest with in item to upgrade your character. Go you your room (the 3rd option on the character select screen). There, you can equip/use the item, and talk to the slave girl. At first you can't do anything with her except talk.
A new set of monsters becomes available the arena. You can fight them, but they are stronger than the previous set. If you're having trouble, you can go back to the first floor of the arean and revive the monsters to grind up your level. The first set of monsters should be super easy now.
After you defeat the second set of monsters, you may get another treasure that you can use/equip from your room. Now you can also have some fun with the slave girl. It's still pretty basic stuff at this point. As you progress through the game, she becomes willing to do more and more stuff (the animations have more stages).
Now you can fight the 3rd set of enemies in the arena. This is where the heroine girls start to show up. You can fight them just like the monsters. They tend to have flashy attacks and some can cast spells or heal themselves. Your grab attack can drain their mana. If you tap the grab attack button again, you can perform a battle-rape animation with the girl. They will regen their mana during the battle-rape, but the crowd will throw lots of gold at you that you can pick up. This is where the game becomes really easy, since you can make a ton of gold by battle-raping the girls over and over.
Anyway, the game continues like that. there's a 4th set of enemies in the demo, with the highest level character being level 22 from what I saw. You can defeat her at much lower level than that though (I did at like level 14 or 15 or so).
Also, the other posters in this thread are right. The Frog is totally OP. It can just stun-lock everything. I played through the first time as the rat man and had to grind, but the second time with the frog was easy-peasy.
Note that each character (the frog, chibi-dragon, and rat-man i nthe demo) each has their own set of items (gear, potions, etc.), but they all share the same gold pool. That makes it much easier to level the other characters. The H-animations are somewhat different between the different monster characters.
Stuff I don't know:
1) How to unlock the other monsters. It's probably not possible in the demo.
2) If there's a way to capture the heroines (to take back to your room) or if there's a way to defeat them without dropping their health to zero. (I've tried draining all their hp or using the trap item, but no luck)