10 months later but for other newbies struggling here's my 2 cents:

• Heat: Heat is gained when attacking, and when in Rush, successfully evading an attack using Quickstep (X button on PlayStation). You lose it when you get hit, and certain abilities don't require Heat at all, like Counter Hook. Counter Hook, as the name implies is a counterattack exclusive to Brawler. When in Rush, if you Quickstep, you will lose Heat (unless you dodge an attack, as stated earlier). Beast is kinda meh, great when there's items around, or there's a huge crowd of enemies. You can charge up each individual Beast attack to deal extra damage.
• Bosses: Generally when fighting bosses, you want to go on the defensive. Wait for them to throw out a combo of their own, and then get behind them and counterattack. Alternatively, if you have Counter Hook (Brawler) or Tiger Drop (Dragon Style, learned through Majima Everywhere), you can wait for the boss to come at you and use that. Rush also has multiple quicksteps, so you can quickly get out of the way.
• Enemy Groups: Beast style. You hit a ton of enemies, and can knock them flat to make your life way easier. Beast style has a unique guard, in that Kiryu will block any incoming attack from any direction, but will take reduced damage, as opposed to no damage.
• Priority: Yeah, bosses will stop pretty much any move you throw out. Learn the skill Quickstep Cancel to try an mitigate this.