For everyone having trouble with combat, the most important thing is to keep buying the Power Up item from the shop in the police station map. They're how you level up your attack power to make encounters easier, or even possible.
Buy lots of them, keep fighting the molester and spend all your money on Power Ups (and rent) for a few days. Once you level up enough to learn Hard Hit, it's safe to go for the drug dealer. But once you defeat the dealer, you'll have to worry about dogs piling up. So I like to have both the MP reduction items from the Power Up shop before defeating the dealer. That way I can go right into the dogs and kill them in 1-2 Hard Hits.
From there, keep clearing the trash filled maps, resting if her lewdness gets high, or strength (should be called stamina) and buying more power ups. The boss of the dog area is really hard, don't go for him too quickly.