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Non-elemental melee attack, combos up to four hits with increasing size
Yawn. Another melee combo attack. Even in Dungeon Trial mode, there's no escaping these attacks. It's cheap, and looks neat, but I find it difficult to hit the same enemy with all four attacks.
How to get it: Accumulate 30,000 Campaign Points in Dungeon Trial mode.
Slash elemental medium-short-range lunging attack
Collbrande is basically exactly the same attack as Treant, but Slash elemental. It could be really handy early in the game, before you get the good Slash elements. Otherwise, you're moving toward the enemy, which may or may not be a good thing.
How to get it: Accumulate 150,000 Campaign Points in Dungeon Trial mode.
Destroy element medium-range attack with wide spread, chargeable
Valiant would probably be really handy for Ellen, but for Keats, it's just another Destroy attack that's way too expensive and takes way too long to be useful. I suppose it could be good for use against groups at a distance, but it has a minimum range, and any Folks that get past that will have a clear shot at you. It's also annoyingly painful to build up. I wouldn't bother.
How to get it: Accumulate 100,000 Campaign Points in Dungeon Trial mode.
Ice element medium-short-range attack, chargeable
Alphard kind of mixes the worst aspects of Exedra and Kraken without the advantages of either. If you can get it before chapter 3, it might allow you to get Bug-a-boo and the items in the locked room in Warcadia early, but that's the only reason I can see for ever wanting to use Alphard.
How to get it: Upload a 4500 point dungeon in Dungeon Trial mode.
Earth elemental short-range dropping attack, combos up to four hits
Quasarilli is one of the cheapest Earth attacks you can get, particularly early in the game, and quite effective. I use it in pretty much every situation where Earth is useful, at least until I get Habetrot for a better ranged attack. I'm quite fond of it.
How to get it: Download it for free from the Playstation store. This only applies to the North American region as far as I know - the European region gets two different Folks in place of Quasarilli.
Destroy elemental attack, chargeable to expand effect area
Maximilian's attack takes too long to charge and isn't particularly useful without charging, so I don't find it very useful. It's handy against large groups if you can be reasonably assured you'll have time to charge it up without getting attacked. Otherwise, if you're not charging it, it's no more effective than Bargest or Ga-dearg would be.
How to get it: Download the DLC pack that includes the "Weapon Destruction" quest. You don't need to complete this quest - Maximilian will be added to your bestiary automatically.