As like with many of the other Yakuza titles, Yakuza 4 also features several Ultimate Battles.
These are usually fitted into several different categories, which are unlocked through the course of the main story.
These specific Ultimate Battles are categorized into the Ultimate Battles (which consists of Brawls and Grudges), whilst the other is the Ultimate Matches category which consists of both the Speed and Trails matches.
If you plan on getting 100% in this game you will need to complete them all. Below are several video guides which will hopefully help you complete these.
ULTIMATE BATTLES (BRAWLS)
ULTIMATE BATTLES (GRUDGES)
ULTIMATE MATCHES (SPEED)
ULTIMATE MATCHES (TRAILS)
Related Guides / Links: