Your next destination is in the upper right corner of the map. Along the way to the second dungeon entrance, you will encounter the Fighter who you must battle and defeat in order to take possession of its body.
Be careful when jumping up through a gap in the ceiling to the area up above. Be sure to hold the jump button down even as the next part of the fortress loads in, and hold left or right, depending on where you want to end up. If you don't do this successfully, you will end up having to sit around while the previous portion of the fortress loads back into memory.
Fighting against the Fighter is pretty much just like fighting against the Bouncer. Get in low, and get in quick, and attack as frequently as you can. Eventually, you will knock the Fighter out, at which point, you will appear to be knocked out as well. However, shortly after, your bodies will switch places, and you will now have control over the Fighter. You will start out with seven units of health.
There are two items you should try to collect once you become the Fighter. One if the power-up item which allows your punches to do more damage, at least to the walls and blue blocks around you. The other is the lamp. In the upper areas of the fortress, the lights will go out, and only possession of a lamp will allow you to continue seeing your surroundings. Remember that the lamp will die out if you spend too much time in a dark area. Also remember that you will waste the use of a lamp if you fall out of an area that needs it before you are finished there.
Take note of the false floors that appear on your way to the second dungeon entrance. Falling through these can become a costly detour as you return to the proper path. Beyond the false floor and the pitfall is a Blaster. In reality, you don't need to deal with it if you choose not to. You can jump over him and continue on your way.
On your way to the second dungeon, use attacks as you jump up the steps so that you do not cross into the screen above you until you are on the highest step. Once you reach this step, perform a full jump while pressing right in order to minimize the amount of loading the game does, and potential lamp usage. Once you arrive at the second dungeon entrance, be aware of the Bouncer that guards the area. Fight him or ignore him, and attack the dungeon entrance to access the next area.
The only enemy that you will encounter in this area is the Magician. Additionally, a lot of the items that you obtain in this area are amulets. Amulets will protect you from one magical attack each. Despite the abundance of amulets, it would be best to attempt to save them up if possible, since you not only need them on your way to the boss, but also on your way back to the fortress.
It is possible to guard against a Magician's attack. You cannot duck beneath it. As you approach a Magician, be prepared to back up in defense when it starts casting a spell at you. Then get inside and punch it. After climbing up the ladders on the right side, you can carefully fall to the right of the Magician to attack it, or leap over it and ignore it entirely.
The statue the appears in front of the last ladder on the left side can be tricky to deal with. You will have to jump to the right and attack it as you fall. After you perform a punch, you can double jump to get back up and over the wall in order to proceed.
The boss that guards the ASOK idol may look fast and difficult, but if you stand on the step to the left of where the boss appears, you can crouch down and safely attack it. It should be defeated after four punches. Then punch the statue beyond it to collect the ASOK idol, and make your way back to the fortress. Beware of the Bouncer who will appear right next to the dungeon entrance as you continue in the fortress.