This page should help us understand the mechanics behind the somewhat undocumented aspects of battle!
To begin, there are 8 different combos: Bellator, Sanctus, Maquina, Alliance, Fierce, Dandy, Saucy and Wild.
Combos can be initiated by certain cards that match the criteria. The higher the combo level of a card (max 200) the higher chance the combo will apply to a card. Note that skills and combos can activate from a card even with low combo levels.
It should be noted too, that the first Pirate in a Team (both Attack and Defense) will always be unable to obtain a combo, as you need 2 cards for combos to activate. That pirate can still activate and receive skills though.
Bellator, Sanctus, Maquina & Alliance Combos:
These combos are activated by having at least 2 of the same Nation's cards in a row. There is currently no "Unafilliated Combo", though. These combos cannot activate multiple times on the same card. These combos boost ATK (and assuming DEF) by 10% each.
Fierce, Dandy & Saucy Combos:
Each Pirate has 1 of these combos attributed to them. In order to activate them, you need to align 2 Pirates with the same combo attributed. For instance, if you align Relentless Atara and Magic Bullet Akira, the 2nd Pirate in that row has the potential to receive the Saucy Combo. If you align Relentless Atara and Battle-wise Athena, neither Pirate will be able to generate a combo, since they have different combo types attributed to them (Saucy and Fierce respectively).
These combos cannot activate multiple times on the same card. These combos also boost ATK (and assuming DEF) by 10% each.
This combo type works very similarly to the other combos, except that it ONLY works for cards from The Alliance nation. For example, if you align Delinquent Yakira and Sage Hume, no Wild combo will activate, since Yakira isn't from The Alliance. In order for the Wild combo to activate on Sage Hume, the card before him would have to be from The Alliance also.
Planning your combosEditWhile you may wish to leave combos to chance and hope for the best, good planning can ensure victory in most situations. If you can combo enough boosts and cannons added to your cards, you can be quite the powerhouse. For instance, if you leveled your cards solely with Mermaid Kiennas, you'll see your combo level is drastically low (see pic to the right). As such, if you had low combo cards, you'd want your teams to consist of the highest base values for ATK/DEF.
However, if your cards have high combo levels, combining Skills and Cannons among your cards will yield far superior results. Case in point: if all your combo levels were 1, a team of 5 Gold Battle-wise Athenas would be your best bet for attacking, yielding 65k attack plus your Skill amount, that could be boosted to 97.5k if all skills activate on all Athenas. However, if your combo levels were high/maxed, a team of 5 Gold Explorer Nerias would yield you the best attack, maxing at 155k if you had 10 Gold Athenas as backup. Unfortunately, this team isn't possible yet, and nobody has that many Athenas, and it'd likely cost you hundreds or thousands of dollars to reach, but you get the picture.
The same applies to defense. Combo level 1 with Athena topping out at 65k, and at max combo level, an even harder to obtain team of 5 Gold Harpos with Gold Athenas as backup topping out at 156.5k.