Remember, to skip dialog, press q on the keyboard.
To defeat the three headed snake: you need the sword from the thief cave. The thief cave opens after the inn owner tells you about the thieves (he tells you something new each morning, so check back with him about five or so times). Go out from town, turn right to the next screen. There should be a shiny point, the rest is self explanatory (might have to be night, was day for me). After you get away from the thieves, go back to the cave, then all the way left, then a switch puzzle.
The order is middle, left, right.
Go through the dungeon (lose once for CG). Fight the boss, who is pretty tough, and get his sword (Feather Blade). It has a 2 point attack but does less damage than Knight's Sword. If you use the special, it will bump sharpness to 6 so you can kill the snake.
There is also another quest you can take to kill an alligator in the sewer next to the park. Nothing major, just 300 gold.
Enabling prostitution: I do not know how exactly. I had no problem doing it. Basically, make sure to kill all the enemies to you can and keep talking to the guy who offers you money for sex (south part of town) since you will not have enough to the boat trip. The C accessory does not seem to influence it. He also has the gangbang (which is the prostitution event) and one more event after that in the ocean.
Goblins: Beat the lizard in the waterfall cave and then fight the goblins inside. Lose, etc.
Guard H: after becoming a prostitute, Guard H will appear near the inn on one day or another. Just talk to him. Also, you may have to do stuff with the other customers before he may first appear but I don't think this is necessary.
Hot spring event: go to the hotspring and encounter men there twice. After that, go into town during the day and find a shiny near the guard building. Remove panties and examine it (you can remove panties after talking to the panty buyer at night near the sewer). Go into hot spring, pick the bottom option to go in naked. Go to the spring itself, choose the bottom option(?) to come out in front of the old men. Then, get caught by the old men in the next screen.
Adventurers: talk to Gide and group at night, agree to stay with them, etc. Next morning, go into the inner forest (with the three branch splits), go right, then right again to the next screen. Here, go up and around right, then down. You will encounter a demon boar attacking the adventurers. Help them, etc. Go back into town, sleep until the next day. Sleep again until night time. Go outside your room (you did this right if Gide and group are not sitting in the bar) and go back in to see another event.
On the island near the western shore, there is also a secret door (like the thief cave) that you can examine. I do not know how to open it or if it does anything.
EDIT: After beating the game, it doesn't seem like there is anything connected to it. I'm sure it's there for a reason though.
If you do everything, and spend a couple of days prostituting, you should get 200K gold easily. Also, make sure not to forget to get the dog collar from and the red flag item from Marie the item seller in the left shop. Also, also make sure to grab the griffin wing after killing the ant on the lowest level of the sand island dungeon (the one near the shore that you swim to).
Going around topless: during the phantom ship battle, the last guy you fight is near a book case. Kill him and examine his spot near the book case to get the nude princess book. Return to the ship, etc. Later, Kate will rest while the sailors remove some rocks. At this point she can read the book. If she does this, you can wear the bikini bottoms and no top for the rest of the island adventure until you return back to the town.
Cyclops: just loose to the cyclops you fight in one of the caves in the island. Pretty simple. You can also lose to him again after escaping.
Sailor event: read the nude princess book and walk around topless. Then, after the sailors get lost, find them all before getting the sword from the pirate captain (there are 7 and they are easy to find). Then, talk to one sailor who keeps trying to kiss you while topless in the base cave and the event will occur. Proceed to get the pirate sword from there as normal and you can still repeat the event.
As for the island itself, I was level 20. The fights are mostly easy if you know the battle system. To get the second best sword, go up, then right up, then into a series of caves to fight the pirate king. Don't do this until you find all possible sailors (7 of them) in order to get the sailor event described above. If you have the feather sword before the island, it should be pretty easy to rescue all the sailors. To get the best sword, you must explore some ruins (and some caves) and fight a salamander with the sword you got. After winning the sword is upgraded to a much better one (7 sharpness, 2 point attack).
To beat the long neck and the t-rex (I was level 22 with best accessories and the upgraded sword): the key is timing and knowing the battle system. Enemies and you take more damage when your AP gauge is low. Enemies do more damage when their gauge is low, you do more damage with successive strikes as you AP gauge decreases. The optional health accessory found in the ruins really helps here because it allows you to carefully heal.
Strike the enemy once, then refill your gauge. When the enemy is taking the most damage (you have to figure this out, it is usually after the enemy attacks thrice in succession or so), give them your full combo. You know you did this right because the enemy will not attack for at least another two turns to refill their gauge. Otherwise, just keep jabbing them with one strike, eventually you will get an opportunity.
Also, don't forget to use your special ability for each battle, it makes you do more damage.
CG room: Like someone else mentioned, beating the t-rex gives you the champion seal, unlocking all the h-scenes. Beating the long neck gives you access to all the CG after beating the game.