Most of the enemies here have high SPR and a lot of magic resistance, except for Oldoa. Unless you have a lot of penetration towards SPR and/or magic attack resistance, it's better to go with slash type damage dealers. It works against most enemies except Glacial, but having DEF penetration can help as well.
A physical barrier breaker unit can be really useful since there are a total of 6 Gil Snappers. They have high CT the moment the fight starts, meaning you can't really kill them before they use harden.
After 3 enemies are defeated, 3 more Gil Snappers will appear in the middle of the map. If you want to clear the "Defeat 3 or More Enemies Simultaneously" mission, then this is a pretty good opportunity since they are closely grouped together. Use your strongest damage dealer that has an area attack to deal damage, and increase their speed with any speed buffs to be able to attack them again before the turtles move away. Time Mages have haste and quickens, Ildyra has LB, or Tidus for Hastega as an example.
A safe and slow method is to stick to the right side (Oldoa side). This is because the Kraken and Glacials won't be doing anything if you're not close to them in the early rounds. Vinera is one of the biggest threat there so you'll want to focus on her first.
After 5 enemies are defeated, 2 more Sanctum Monk snipers will appear on both sides of the map.
Side note: This mission is mostly to completely max awaken the Kraken VC by completing all the missions in a single run, but you can get Kraken VC shard as drops from Brutal difficulty or High Difficulty, so completing Nightmare isn't necessary.
The enemies in the quest uses many different attack types, and also do physical and magic attacks. Whisper or Warrior of Light are good at dealing with them, but you'll still need plenty of defensive setups from gears or VCs. You don't need to bring all 3 defensive VCs, since it depends on what your team can handle.
Arithmeticians have a disable inflicting area spell, which is mostly just for the turtles. Disabling them makes them unable to attack or use abilities. Since there are 6 Gil Snappers in total, it can be quite worth bringing an Arithmetician just for this role. There's also Livialle, or Mariale for MR Arithmeticians.
The Gil Snappers are in height 4, this means that if you want to increase the chance of inflicting disable, you'll want to equip height 3 to 2 passive. Increasing your unit's faith also increases the chance of inflicting status effects.
Ildyra's LB increases CT for your team once, which can really help in the early turns, while Helena can be another magic damage dealer since she has plenty of magic/spr penetration.
Ayaka as the main healer since her LB can remove stop, which can be pretty fatal to your team unless it hits your tank and they're tanky enough. Otherwise, you can bring any other healer and equip them with Frederika's TMR (Victory Ribbon) to remove stop when you need it.
Slash type damage dealers works better than other types due to enemies' weaknesses. There are plenty of slash attackers, but the one that has DEF penetration or barrier breaker can save a party slot or two.
Duane pretty much fits the bill for this quest. He hits hard, has DEF penetration, and his barrier breaker move is a small area attack that can potentially hit all Gil Snappers if they're grouped up.
Some offensive VCs if you want more damage is to bring killers/eaters of their type on top of the usual atk up and slash atk up. Titan VC has man eater to go against Oldoa's side, while Greetings from Afar has Aquatic killer against Kraken and Gil Snappers.