The battle divides itself into naturally into 5 parts. Everything up Mourning Wood, Mourning Wood to Pumpking, Pumpking alone, multiple Pumpkings, and the Final Wave.
First, Turn on any heart statues you have. So the hearts/candy apples are spawned at the start of the battle.
Priority 1 is to do over 500,000 damage in 9 minutes, to this end, never take your finger off the trigger, except to get the shroomite bonus early on and to re-up on potions. Priority 2 is to stay alive until you get your trophies.
Try to avoid flying up so far from your death traps that you despawn all the smaller enemies. Basically, if you can hear the death traps you are probably safe. Sometimes it can't be avoided though, later on you may need to fly really high when there are multiple Pumpkings.
Battle part 1: To Mourning Wood:
Turn on your traps and set yourself next to the Grandfather clock and check the time. At 7:20 use your potions. Remember potions are: swiftness, ironskin, regeneration, battle and pumpkin pie. Use the medallion as close to 7:30 as possible.
Stand still to get the Shroomite bonus and fire your weapon of choice towards the sides of your arena, and down into the pit as Mobs appear. Once Mourning Wood appears, do your best to stay still, but dodging it's attacks has priority. You will need health for Pumpking.
Battle part 2: From Mourning Wood To Pumpking
Continue to spend your time near the bottom of your arena, dodging flame spikes and flame jets from Mourning Wood. This is a good time to grab any hearts from heart statues you may have set up. Do your best to get the shroomite stealth bonus, but remember that staying alive is priority. Poltergeists are the most annoying enemy here, because they have a ton of health, yet aren't worth killing. Try to knock them off any platforms into the death traps.
Battle Part 3: From Pumpking To Multiple Pumpkings
When Pumpking appears take to the skies and kite like you have never kited before. Read the Pumpking Tactics list above, and focus on yourself and your characters position in the sky. It is much easier to dodge if you focus your character, not on Pumpking. NEVER stop moving. When you lose your flight and begin gliding, drop as fast you can onto a platform to recharge your flight. However, if Pumpking is in one of his two slower phases, gliding downward can give you an excellent platform to rain death on him.
Try to kill Pumpking in such a way that it's candy apple drops fall on platforms. Avoid these if you have more then 300 health. Save these for when you have potion sickness.
Try not to fly so far away that you can't hear the death traps on the ground.
Your potions will probably run out sometime around now. Quickly get them back up. You will need them for when multiple Pumpkings show up.
Battle Part 4: Multiple Pumpkings to the Final Wave.
Once a second Pumpking shows up, try to goad them into a position where the Pumpkings are stacked on top of each other, so that your weapon is able to damage both at the same time. This allows you to double the damage you are doing. Remember to think about this battle as a battle against one boss with 500,000 health, not as many separate mobs.
Continue to dodge like a mofo and try to get into a pattern where you kill one Pumpking, collect his drops to regain your health, and then kill the other one. Always focus on the Pumpking with the lowest health. If Pumpkings do not spawn for a several seconds, drop down and blast anything on the ground you possibly can.
At some point you will probably be forced to dodge so high up you despawn everything in your death traps. Don't worry about that anymore, just get lower when you can and stay alive.
If you die at this point, don't give up, you might be able to come back. Quickly get your potions back up and drop down from your bed. I put a heart statue over my bed and make sure it is on before the battle to get some extra health in case of death.A very important trick:
The spiky ball death trap ground will be littered with hearts/candy apples. If you get low on health it can be very worth it to drop down on your spiky ball traps and collect them. You will take damage from the spiky balls, but you should gain more health then you lose.
Battle Part 5: THE FINAL WAVE.
The moment you see the FINAL WAVE notice appear, your goal is to kill a Pumpking. Target whoever has the least amount of health. Remember, that all you have to do is kill a Pumpking after the notice flashes. If the notice flashes and there is a Pumpking with 1200 health left, all you have to do is reduce him by that 1200. Once you Kill a Pumpking, ignore all the rest and drop down low enough to try and kill a Mourning Wood. Fire as many shots as possible at a Mourning Wood, and remember that if you die your traps may finish the job.
You will most likely die during this wave. That is fine if you have killed a Pumpking or a Mourning Wood. At least you have your Trophy.
You may have to do this battle twice to get both trophies.