Tip: Make a party with two of the required characters + a fast group damage dealer like Faris/Agrias/Squall/etc and you can clear those missions while you are farming the required monsters.
Another Tip: The next Event or Lost Chapter will probably have lots of these monsters too, so if you are not in a hurry you can get a head start by completing it before tackling these missions.
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Dark Lord x20, Bomb x50
Rydia’s Lost Chapter: Overcoming Sadness pt. 11 (Normal difficulty) has Dark Lord (x2) and Bomb (x4) in 4 waves. Run it 13 times to complete both objectives at once.
(You will get a few more Dark Lords than needed, but it’s still faster than moving to another stage for bombs alone!)
Death Machine x30, Nightmare x20
Cid’s Lost Chapter: Space Dreams pt. 13 (Normal difficulty) has 3 Death Machines and 2 Nightmares in 3 waves. Run it 10 times to complete the Death Machines and get a head-start on Nightmares.
Nightmare x50
Story Act 2 Chapter 1: 1-20 Miasmal Holy Ground Pt.1 (Normal Difficulty) has 5 Nightmare (x5) in 3 waves. Run it 10 times to clean up the last Nightmares you need for this objective.
Alternative: if you don’t want to go through Act 2 Ch 1 yet, Noctis’ Lost Chapter Stage 6 has Nightmare (x4) in 4 waves.
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December Winter 2
Killer Bee x 70
There are so many Killer Bees in the new story chapter, you will have this objective complete before finishing it in normal mode. But if you want to rush it:
Act 2 Chapter 6 – Quick Encounter Pt.1 (Normal difficulty) has 3 Killer Bees in 1 wave, allowing you to finish the objective in around 20 fights (since you will have already killed some bees just in order to unlock this stage).
Bonus: if you want to go a little further into the chapter and combine the bee-killing with Mindflayer hunting, go to…
6-13: Wooded City Pt.2 (Normal difficulty) for 7 Killer Bees and 2 Mindflayers in 5 waves.
Chasers x 30
Another one that you will complete automatically just by playing through the chapter in normal mode, but if you are in a hurry or don’t want to delve too deep into the new chapter:
Act 2 Chapter 6 – 6-10: Striving for Paradise (Normal difficulty) has 3 Chasers in 3 waves, completing it in 10 fights (and giving you a bonus 1 Lamia per fight.
Alternatively, you can find 2 Chasers in the current c0-op event Invader of Ruins: Intermediate, which can be easily soloed. (credit)
Mindflayer x20
This is the last objective that you will get mostly complete by simply playing through the whole chapter in normal mode, netting at least 12 kills from the normal stages. You can farm the rest here:
Act 2 Chapter 6 – 6-12: Wooded City Pt.1 (Normal difficulty) has 4 Chasers in 4 waves.
Lamia x40
Alisaie’s Lost Chapter: Another Realm Pt. 4 (Normal difficulty) has 4 Lamias in 4 waves. You will easily get 12+ Lamia kills completing the new chapter, but that is far from enough to complete the objective.
Alternative location:
Story Act 1 Chapter 3: A Shadow at Shore Pt. 2 (Normal) has 3 lamias in 1 wave.
Santa Gigantuar x10
Only found in the special Winter co-op event.