Hi! It sounds like you are underlevelled. At what point in the game are you? There are items that increase stats, and triggering adult scenes also gives stats upgrades. There's also a light armor that doesn't have the speed penalty.
Hi! This quest's steps are as follows:
1. go to the fort to the east of the dam.
2. inside the fort, make your way up/east and watch a scene (you can get further up through the backdoor).
3. the dam can be entered now. head north along the dam and jump up the debris and enter the dam's interiors, climb upwards and push a switch to pump water upwards to the area with the debris, then you can use the water to go further north.
4. head through the dam's insides to get further north, slide through the moving cogs.
5. boss battle!
Let me know if you need more details.