Characters:
Beat Crocodile in Luffy's adventure mode to unlock Buggy and Mr. 0 Crocodile's adventure mode, continue with Luffy's adventure and defeat Eneru to unlock Chaser's adventure mode.

Nico Robin: I
n Luffy's adventure mode, use her once in battle after she joins the crew.

Red-Haired Shanks:
In Buggy's adventure mode, use him once in battle after he joins the crew.

Portgaz D. Trace:
In Buggy's adventure mode, use him once in battle after he joins the crew.

Mr. 2 Bon Clay:
In Mr. 0 Crocodile's adventure mode, use him once in battle after he joins the crew.

Ohm:
In Mr. 0 Crocodile's adventure mode, use him once in battle after he joins the crew.

Eneru:
In Mr. 0 Crocodile's adventure mode, use him once in battle after he joins the crew.

Chaser:
In Chaser's adventure mode, get Chaser to Lv. 15 and use him once in battle.

Kuina:
In Chaser's adventure mode, get Kuina to Lv. 15 and use her once in battle.

Zeff:
In Chaser's adventure mode, get Zeff to Lv. 15 and use him once in battle.

Hawk-Eyes Mihawk:
In Chaser's adventure mode, use him once in battle after he joins the crew.

Support Characters: In adventure mode, use a support character in 3 battles, then they can be used by any character in Grand Battle mode.

Unlocking Extra Costumes- Straw Hat Pirates:
All Straw Hat characters but Vivi start with their 1P and 5P costumes, and in Robin's case the 4P as well. In general, 4P costumes will be found first, while 2P costumes appear later in the game and are more complicated to get. Any costumes unlocked in Adventure mode will be usable in every other mode.

In unlocking Luffy's 2P costume, make sure not to fight Crocodile until after you have travelled to Jaya and are prompted to finish Crocodile before proceeding, or your game will end at the Crocodile fight.

An easy way to beat Ace(Trace) with Chopper in the Graveyard of Ships is to use Chopper's "Health" attack (Jump+O) non-stop. Beware of rolling bombs.

Luffy 2P:
Obtain the bonus item "Pirate Coat" by beating Crocodile the first time at Alubarna in the Alabasta Kingdom Sea area with a super attack

Luffy 4P:
Obtain the bonus item "Cool Shades" by beating Buggy with an item at Orange Village in the Orange Village Sea area

Zolo 2P:
Obtain the bonus item "Goggles" by beating Arlong at Spice Village in the Jaya Sea area

Zolo 4P:
Obtain the bonus item "Necklace" by staying alive for 30 counts against Hawk-eye Mihawk at Blue Town in the Syrup Village Sea area

Sani 2P:
Obtain the bonus item "Gaudy Shirt" by beating Don Krieg at Vinegar Village in the Jaya Sea area with Sanji

Sanji 4P:
Obtain the bonus item "Necklace" by beating Chopper at Big Horn in the Drum Kingdom Sea area with Sanji

Nami 2P:
Obtain the bonus item "Yellow T-shirt" by beating Buggy at Vermillion Town in Jaya Sea Area with Nami

Nami 4P:
Obtain the bonus item "Fashionable Sunglasses" by beating Chaser at Navy Base No.64 in the Inshore Alabasta Kingdom area

Usopp 2P:
Obtain the bonus item "White Bandana" by beating Kuro at Mock Town in the Jaya Sea area

Usopp 4P:
Obtain the bonus item "Sunglasses" by beating Nami at Coco Village without knocking her out

Chopper 2P:
Obtain the bonus item "Santa Hat" by beating Ace(Trace) with Chopper at a Wrecked Ship in the Graveyard of Ships

Chopper 4P:
Obtain the bonus item "Panda T-shirt" by beating Nico Robin with Chopper at Erumalu in Alabasta Kingdom Sea area

Robin 2P:
Obtain the bonus item "White Hat" by beating Ohm the first time at the Ruins in Skypiea

Luffy 3P:
Obtain the bonus item "Baseball Uniform" by beating Luffy with more than 30% HP at Mustard Village in the Fusha Village Sea Area

Zolo 3P:
Obtain the bonus item "Judo Wear" by beating Zolo with a super attack at Red Town in the Fusha Village Sea Area

Sanji 3P:
Obtain the bonus item "Soccer Uniform" by beating Sanji without jumping at Carmine Town in the Orange Sea Area

Usopp 3P:
Obtain the bonus item "Chestpiece" by beating Usopp without getting knocked down.

Nami 3P:
Obtain the bonus item "Cheerleader" by beating Nami with more than 70% HP at Coco Village in the Roguetown Sea Area

Robin 3P:
Obtain the bonus item "Kimono" by beating Nico Robinwith more than 50% HP at Misty Peak in the Drum Kingdom Sea area

Chopper 3P:
Obtain the bonus item "Polo Shirt" by beating Chopper in 20 counts at Pepper Village in the Drum Kingdom Sea Area