Oh those are カツアゲ, basically giant extortionists, they might seem tough to beat but they have rather simple attack patterns, its best to not get greedy with attacks early till you get strong later on, its a good idea to carry around different weapon types for heat actions on them to take them out faster(knives, bats, clubs) or fight where they are a lot of items to pick up(bikes, traffic cones, neon signs) but remember repeating the same heat moves on them reduces the amount of money you get, so vary it up if you can(also never try to grab them).
For Kiryu his thug style early on is great for them, can use square and then triangle for a one-two combo or can do more hits in after their windup backhand move, for Majima his street fighter style is also great early on for a one-two combo, plus you can get a free heat action once you unlock slugger(bat) style with him. Their jumping grab move would be impossible to survive at lower levels so avoid if possible, they also gain more life and money as you beat them also they get enraged faster.
In the 2nd section of the CP list, you can unlock the ability to gain more money from them(and enemies in general), plus if you do get beaten up there's a chance you'll find them sleeping somewhere and can drain them of their money(kinda slow) or wake them up and usually they would have reduced health. You can also get an enemy finder item that would show enemies on the map, allowing you to hunt them down way easier.