Hey Look, It's a Harkon Guide! This is pretty much for listing what monsters you should prioritize over everything else.
There are three mode's to Harkon. I'll list them by the order they are listed on GGFTW's wiki.
Mode 1 - The easiest mode. First wave is extremely easy, prioritize c1/3/4, as they get the most monsters. Try to ensure 1 takes as few dmg as possible. Second wave is concentrated on c1, other crystals sometimes get large concentrations. Wave 3 is concentrated on c3/c4. Bosses will spawn behind the crystals in the corners, c1 will not get bosses. Once bosses start spawning its recommended to ignore the front spawns becase they do relatively little damage in comparison.
Mode 2 - The boss rush. Bosses get a large health boost, and have somewhat different skillsets. Priorities are a bit different here. C1 gets the largest concentration of the more dangerous bosses, c3 and c4 has larger concentrations of Scylla, while c5 and c2 gets more Charybdis.
Mode 3 - The gloomy mode. First wave is easy at first but expect some deaths at the gloom warriors, since their siren song can hit up to 14k and they WILL spam it. 2nd wave is unlike mode 1, concentrated on the corners, usually 3 and 4 again. Final wave is just a huge rush from the front. You must defend the crystals until 2:30. It is imperative that you prioritize killing the more dangerous monsters first (I.E. its ok to let mummies through, but not gloom warriors or bosses.)
Regardless of mode, expect werepots. They can kill you even if you forget to refresh minds eye, but if you dont stand next to the crystal they're harmless.

- Let's start with this...the very sexy Gorgon. On Modes 1 and 3 she is by far the most dangerous monster in the defense. Under berserk her Tetra can hit upwards of 400k on players and can 3HKO a crystal. This monster MUST be killed first and fast on these two modes. They are weak to guns. On mode 2 she changes to a charm type skillset. She does a lot less damage overall but she carries wink which is very annoying to spellcasters. She is weak to magic and is overall the least powerful monster in mode 2, and should be ignored until last.

- Second we have the cowboys, Charybdis. They are relatively the same across all modes, except with more health on mode 2. Their notable trait is that on all modes they carry armor destructor, which makes everything ELSE kill the crystal faster, so they should be killed second. They also have the highest movement speed of the bosses, and will actively run away if you stand next to them because they use ranged attacks. In Modes 1 and 3 they should be handled by magic easily, but keep in mind you need around 360 lk to hit them with AR constantly. On Mode 2 they are weak to guns, and are HIGHLY resistant to non-attribute attacks other than guns.

- Third are the golems, Scylla. They are the slowest boss, usually takes 6-7 seconds to reach the crystal from their closest spawn point. In modes 1 and 3 they are relatively harmless to the crystal itself, but their use of siren song hurts a LOT. In mode 2 they are the power type, doing the highest base damage and they CAN use inferno blade and berserk if their health is low so be careful. They are a low priority target in modes 1 and 3 but should be killed by melee immediately after killing Charybdis in mode 2. In all modes they are weak to physicals and are HIGHLY resistant to magic, so much so that in mode 2 its futile to try killing one as magic unless you're a SM or are water/elec.

- Last we have Hecate, whose hat everyone wants. XD These ladies are highly dangerous to anyone without high MD, as in all modes they use pure sheep 3rd job spells like staff of thunder, as well as dark lance. Be especially careful if you're not magic, as they also use dark barrier, which will quickly kill you if you don't kill them before they reach the crystal. Overall they're the 2nd most dangerous to players, but they can't really hurt the crystal so its ok to leave them alive if something more dangerous such as gorgon is alive. On all modes they are weak to guns (ggftw claims on mode 2 they are weak to light but that's a lie).
What are other monster's with high kill priority?
In mode 1 you should kill Kira of Sense and Guardian of Power before the others if given an option and don't have AoE.
In mode 3 you should kill Gloom Dolls and Gloom Warriors before the other two gloom fodder.
Other things to remember:
1. Do not forget to bring pots.
2. Mages, make sure you keep the non-mages on a crystal you're sharing alive. If they stay alive, you stay alive.
3. Remember to refresh your buffs and especially minds eye before they expire. It would suck to have scorching down and not hit anything because you forgot to refresh the skill you need to hit the monsters. XD
4. Learn how to force your guardian onto a monster by right clicking them. This is very important in boss mode when more than 1 Charybdis is at your crystal because the guardian can keep one from doing anything while you kill the other.
IMPORTANT MONSTER SPAWN TIMES
Mode 1 Wave 2 boss spawn times: Charybdis - 11:00, Scylla - 9:40, Gorgon - 8:15, Hecate - 7:00
Mode 1 Wave 3 - Bosses spawn behind crystals at 4:40. Gorgon doesn't spawn until the 3rd spawn. They come 1-3 every 10 seconds.
Mode 2 - Auto Faint - 17:00 Charybdis Waves - 15:30-14:00 \ 13:00-12:00
Mode 3 - Wave 2 Boss Times: Charybdis - 8:15. Scylla - 7:35. Gorgon - 7:00. Hecate - 6:30
This is all, I'll amend it if I feel it needs to be!
<3 from Mira.