Check the in-game Notebook for a variety of useful gameplay tips not listed here.
There is no autosave, so make sure to save often.
Hold X to dash and R1 + X (or whichever equivalents) to fast forward text.
When you first get to move freely in the city in Chapter 1, stock up on some healing items from the drug store to make an early boss fight easier.
Strike a balance between side activities and story progression, side stuff becomes easier and more worthwhile after you've at least unlocked each character's business and the ability to avoid street fights with Cash Confetti.
Making the right choices in sidequests earns you better rewards, but you're not permanently locked out of anything critical even if you goof around - Dream Machines will stock any special rewards you miss.
In general you cannot permanently miss anything except for a handful of story trophies/achievements which you can get on New Game+. Once in the endgame or in the "Premium adventure" mode unlocked after beating the game, you can switch between protagonists at will by using the phone in their respective businesses.
Both characters have separate CP (Completion Point) pools used to unlock gameplay bonuses, so you can't "save up" with one to have more on the other. The clown near the CP exchange shrine offers free and powerful DLC items, also separate for both characters.
Don't bother grinding random enemies for money as the business management systems you eventually unlock are a magnitudes better source of income.
If you really want to swim in cash, Mr. Shakedown becomes the ultimate moneymaker once you've unlocked Kiryu's "Mr. Shakedown's Deep Pockets" with CP - as he then gives out more money than he takes, one can simply alternate between beating him and losing to him to gain ever-increasing amounts of yen. Having a Zap Gun or two is recommended.
Your combo finishers vary depending on how many normal attacks you do first. Some are more useful than others, so try out combos of different lengths.
A lot of weapons and situations (such as fighting with a partner or near certain objects) come with unique Heat actions, so try out different things. Note that you can't pick up environmental objects while in Kiryu's Rush or Majima's Slugger styles.
Bosses and other extra tough enemies are fond of counterattacks and are hard to keep pinned down, so it's often better to adopt a hit-and-run strategy and keep your combos short against them, in turn striking whenever their own attacks leave them open.
Repeat use of the same Heat action greatly reduces the damage it deals, so either change things up or simply maintain high Heat for the passive power increase it provides.
Don't dismiss each character's group battle style (Beast and Breaker) against solo enemies as their damage output is considerable. For example Beast lets you repeatedly grab and slam an enemy to the ground, and one of the Breaker combo finishers deals massive damage to a grounded opponent.
Abilities & Equipment
To learn new moves from a teacher, you need to have unlocked an ability next to one of the 'M' spaces in the ability grid. The locked outer rings of the ability grids are opened by progressing in each character's respective business storylines.
To use a weapon, first equip it from the menu and press "down" in combat to take it out.
Some equipment have special properties, hinted at in the descriptions. For example the Charismatic Autobiography will attract more fights, while the Quick Change Clothes lets you switch combat styles on the fly.
Majima's weapon search side activity can net some really cool equipment, but getting serious about it also takes serious cash and is ultimately more of a luxury than anything. Crafting equipment once makes it permanently purchasable, but finding specific parts from the numerous locations and agents is kind of a pain without a guide.
While initially unmarked, a weapons store opens up for Kiryu in Chapter 5 located in the Kamuro Shopping Area, allowing you to buy, sell and repair equipment there. Any gear crafted as Majima is automatically added to this store's stock as well.
Disco can be tricky, but at its core it's just karaoke with a busier screen except you also need to have the cursor on the right tile before pressing the button. Focus on maintaining the combo over worrying about the step amount, and most importantly avoid "stepping off" the grid as this momentarily stuns you.
Darts and Fishing are both much easier once you have high-quality darts/pole to use for them. Both Sotenbori River and Kamurocho Pier have two different spots you can fish from with some unique fish for each. Quality Bait or better is required for some rare fish.
Pocket Circuit Racing is largely a matter of cash and finding the right balance for each circuit, Dream Machines and various shops stock the best stuff. All cars are identical except in looks, only the parts matter.
Catfighting is mainly a game of chance, sometimes no amount of mashing can win you the RPS clashes. The odds and scrolling text in the bottom gives some indication on how well each girl is likely to perform, but mostly it's a matter of picking one of the strong ones, aiming for your opponent's weaknesses, and hoping for the best.
The Telephone Club holds 7 completion log entries depending on which girl you hook up with, three of them friendships and four failed dates. There's no sure way to tell whether you're calling someone you've already called before ahead of time though, beyond recognizing their voice and them always wearing one of the three bikini colors. You can always hang up by holding L1.
The business side activities are unlocked in Chapter 5 for Kiryu and Chapter 7 for Majima and while not 100% critical to beating the game, they are quite rewarding in terms of money, substories, and opening up the characters' ability grids.
The skills/looks of your advisors/girls for each respective business are represented by symbols; from best to worst they go Double Circle > Circle > Triangle > Cross.
While most businesses can be acquired/partnered with simply by walking next to them with enough money, some (such as the arcades) require first fully befriending a staff member inside.
The "Business" tab in your menu lists all businesses you have not yet acquired/partnered with in a given area, though it won't give their precise locations.
Real Estate Royale
Completing side quests and befriending people often unlocks new advisors, managers and security personnel for Kiryu's business.
Don't bother assigning staff and collecting from areas you have no real income from yet, and keep decent initial security in places you do collect from to avoid troublemakers. Troublemakers stop appearing once the area's owner has been defeated, after which Security rating only affects the number of random enemies in that area.
Cabaret Club Czar
As with Kiryu, completing side quests and befriending people often nets you new hostesses for Majima's club.
The best outfit combos for your Platinum Hostesses always give them 3 Double Circles and 1 Cross in their looks. Until you unlock more Platinums, having two such sets saved for each girl makes it easy to switch around as needed, though ultimately their conversation stats (only increased by levels) have a higher impact than their looks.
Time stops when assigning a girl to a table, so you can take your time checking the customer's mood for each girl first.
Memorize the hand signals given by the girls when they ask for help as getting the requests right consistently is a big help in the long run. Most are fairly obvious.
There are 3 levels of Sunshine Fever, so it can be worth waiting to use it until the meter and your tables are full, though primarily aim to use it whenever there are a lot of guests who aren't about to leave. Triggering it during Rival Battles also drains your opponent's ability meter some.
How well you do in the Special Training conversations with each Platinum Hostess is not hugely impactful, good lessons just net more experience than bad ones. All the conversations with a girl can be reviewed at will once you've done them all, in case you're curious about any choices you didn't pick.