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Non-elemental melee attack, combos up to four attacks
For Keats, Hawk is an analogue to Pouke with less horizontal range, but slightly more speed, and considerably more likely to score multiple hits with each attack. All four of its Karmas can be unlocked in this chapter - since Pouke has to wait until chapter 4 to reach that point, it might well be worth switching over.
How to fight it: Hawk is the Pouke of Warcadia. Its main strength comes in numbers, as it can charge from quite a distance, and if you're surrounded, you're likely to take hits. Keep moving to avoid its charges and attack with absolutely anything that suits your fancy - Fire is particularly effective.
Non-elemental long-range projectile attack, combos up to four shots
Bullseye is a quick, effective long-range attack. It can be difficult to target without the aid of lock-on, but why would you fight without lock-on? Its damage isn't too impressive, but it hits about as hard as Pouke from a distance. Once you've captured enough Bullseye to unlock its full combo, it's useful for shooting at enemies that are moving toward you, dealing a bit of damage before they get into range of a stronger Folk. It's pretty useless when you're surrounded, though.
How to fight it: The only real advantage that Bullseye has over Hawk is that it doesn't have to move to hit you from a distance. If you keep moving, it will have a hard time hitting you, and it only shoots occasionally. Block or dodge its attack, then move in for the kill (or capture).
Non-elemental medium-range projectile attack, rapid-fire shots that can be aimed freely
Barrager's attack is pretty weak, but the number of attacks it can deliver is unrivaled. You can aim it even while locked-on, allowing you to use it effectively against small groups of Folks in addition to its limited effectiveness against single enemies.
How to fight it: Barrager is pretty much a Bullseye that shoots more bullets at once, making Killmoulis completely useless. Your best bet is to try to get behind it and hit it with Fire or any other convenient attack.
Fire elemental short-range attack, steady stream that can be aimed freely
Volcano controls a bit like Barrager, but with a shorter range and a higher MC cost. Like with Barrager, you're pinned in place while using it, so unless you're attacking a target that's going to stay stationary for a while, I don't see much advantage to using Volcano over Hinky-Punk.
How to fight it: It's probably easiest to take out the squadron of Hawks it summons first, since Volcano can command them in a coordinated charge that can be tough to dodge. (If you have Patriot, that's a bit less of a threat, but it's still best to take them out first so you can capture Volcano in peace.) Its flame attack is easily dodged by backing away, but can be blocked with any shield. It also launches cannonballs from a distance, which can be dodged if you move quickly enough. It tends to fall down after this attack. Keeping your distance and shooting with Bullseye is a pretty sound strategy, but getting in close and using an elemental attack like Hinky-Punk or Poury can work well. Capture it with the Beat method.
Destroy elemental medium-range projectile attack with area effect
Brummbear is a solid choice for the Destroy element - it's got enough range to keep you out of the way of most threats, enough power to cause some damage to most enemies, enough of an explosion to hit even if you're a bit off with your targeting, and a low enough arc that it isn't likely to go over the heads of your enemies like Gargantua can. It's a bit on the expensive side, but generally worth it whether you're fighting one enemy or many - you can usually buy enough breathing room in the two or three shots you have to wait for your MC to recharge.
How to fight it: Brummbear is basically a Volcano without the flamethrower - take out any Hawks that are around and hit it with whatever attack you have handy. Unlike Volcano, Brummbear is vulnerable to Destroy element attacks. Capture it with the Beat method.
Destroy elemental short-range jab attack, combos up to four hits
If you're going to fight a Folk that's vulnerable to Destroy from close-up, Ga-dearg is a solid choice. It's also useful for picking away at enemy health between uses of a stronger Destroy attack. It's narrowly-focused, though, so if you're surrounded, you might want to use Bargest for a wide sweep or Brummbear to hit enemies with the explosion.
How to fight it: Ga-dearg is only vulnerable to the Destroy element, but Keats has plenty of options for that by now. Brummbear and Ga-dearg are probably the easiest to use, although there's a spot in the room where Ga-dearg first appears where you can stand above them and rain Gargantua attacks down on them safely. If you're not able to get out of range, Ga-dearg will try to stab you or charge at you - neither attack is much of a threat if you're paying attention. Just don't let a group of them surround you or get off-screen.
Frontal shield
Patriot is incredibly expensive until you unlock its Karmas (at which point, it's only reasonably expensive), continuously drains your MC on top of the cost to summon it, and only blocks attacks in the direction Keats is facing - you can't move while it's active. Its main advantage over Killmoulis is that it can block any number of attacks as long as your MC holds out. Just don't drop it too early, because summoning it again will leave you pretty empty. It's a good choice against most enemies that have combo attacks or any sort of rapid-fire attack, but less useful in groups of enemies, where Keats is likely to be attacked from behind.
How to fight it: Only Destroy attacks are effective. I recommend attacking its back - not only will you be out of range of both its melee and charge attacks, but it can't block your attacks from that side - a fatal weakness.
Destroy elemental medium-range projectile attack with a high arc and a small but tall area effect
Gargantua is a TANK. Built up to full, its power is almost off the chart. It's slow to fire, but not too hard to aim - the shell seems to land on the targeted Folk pretty accurately. On the plus side, even if you undershoot your target or miss by a bit, its shell has a decent explosion when it lands, which will hit almost anything above the point of impact. You can hit flying things directly with the shell, or just aim below them. You just need to watch for enemies moving toward you - the shot will usually go over their heads.
How to fight it: Keats has plenty of Destroy element Folks as his disposal by now, giving him plenty of options. Attack its legs first, preferably with Brummbear or Ga-dearg, to disable its charge attacks. Don't stand in front of it, where it can target you with its shells. From the sides, it can hit you with machine gun fire, but you can block that with Patriot or just retreat to a safe distance. Once it's pinned down, any long-range Destroy attack will work - Andraste and Gargantua are good for that. Capture it with the Beat method.