The Boss Battles refer to a sequence of events where the player must battle and defeat a certain number of powerful enemies, in this case the Dark Purveyors. Each boss will use different tactics to attack the player, and will usually improvise them if the player manages to progress.
The Finishing Strikes refers to a set of QTE's that occur in a majority of Lollipop Chainsaw. These are used to either transition the player into later stages of the fight or end the boss battle with a weakened/defeated boss.
The player must establish the QTE in order to progress, by pressing (Y/Triangle) towards the boss and thereby press it repeatedly while at the same time moving the analog stick towards the direction of the Chainsaw.
Killabilly does have QTE's but they are rather more a counter than an actual strike.
Zed: When battling Zed, the player must be evasive, as Zed is unusually agile and can do great damage to the player if they fail to counter a swift attack. Use LB to monitor many of Zed's attacks.
Zed: When encountering one of Zed's Profanity Blasts the player can either evade or strike the words in order to avoid certain damage.
Zed: When summoning his speakers, destroy the speaker Zed is standing on in order to prevent him from summoning more. Evade by pressing (B/Circle) if you don't want to get hit by his Mohawk Discs.
Zed: Zed's most vulnerable area is his back. Evade a Microphone Stab and begin sawing his back while he slowly reacts.
Vikke: Vikke cannot receive damage while charging up, evade this attack while you still can.
Vikke: Keep yourself at a safe distance from Vikke, being close will give him the chance to shock you with his axe, even closer and he will smash on the floor.
Vikke: Once at the Second phase, be cautious of Vikke's legs, they will return after you weaken them. Press (B/Circle) once they appear to attack you.
Mariska: Mariska's Bubble Blasts can be paused in between teleportations if the player is quick enough to hit her before she conjures them.
Mariska: In the Second Phase note that one of the Mariska's cannot attain damage. Keep focus of this one, as this Mariska will conjure Bubble Blasts.
Mariska: Mariska's Tractors can be easily ignored if the player is fast enough to jump out of their reach.
Mariska: Mariska's Giant Hand in the third phase cannot receive damage. Just evade the attack if it gets too close.
Mariska: The Butterflies of third phase can drain the health bar of the player. Press (B/Circle) to make them come off.
Josey: Josey may slam his Mini UFO to the ground, making him vulnerable to attack.
Josey: Josey may conjure Neon Elevators to appear. Use these stairs and shoot Josey from that distance while he throws his bombs. Be cautious though as Josey may cause the floor to collapse and the player may receive damage from the bombs.
Josey: Save some Blaster Bullets for Phase 2, so the player will not need to counter Josey's Electrical Discharges on the bolts.
Lewis Legend: Lewis may frequently enter the arena to boast about his radical biking skills. Find an opportunity to hurt him during this time.
Lewis Legend: During Phase 2, Lewis may hit a column, causing him to become stunned. Hit him while he is stunned.
Lewis Legend: During the last phase, Lewis may fire rockets towards the player. Run towards him while the rockets miss and giving you the opportunity to give damage to him.
Killabilly: Move Killabilly's arm by pressing (B/Circle) to avoid his spit attacks.
Killabilly: Don't worry about ammo, it will fly towards the player when it depletes.
Killabilly: Killabilly's weakest spot in Phase 2 is his fingers. Hit enough to take him down and you may even earn an achievement.