世界の偉大な海の王だ 
全てのトロフィーを獲得!

King of the majestic oceans of the world!:
All Trophies acquired!

 冒険のにおいがするっ 
最初のルフィのアクションに成功した

I Smell Adventure!!:
Successfully completed your first action with Luffy.

Unlocks as soon as you start up main log and you start the QTE (Quick Time Event) with Luffy where he's swinging from tree to tree.

 仲間になってくれよ! 
はじめてスキルを出現させた

Join us:
Activated your first skill.

When your character has reached lvl 9 go to the episode select menu, open the menu  and choose コイソ セシ ト to enter the coin set menu. On your left should be a bar with 3 open slots, by now you should have 3 Straw HatPirate coins (first 9 coins). Put 3 of them in the slots and you have established your first skill 麦わらの一味. 

 “2年後” 
最初のステージをクリア

"2 Years Later": 
Cleared the first stage. 

Complete the first episode of the Main log. 

 ぶっ飛ばす! 
初めて弱点に攻撃して気絶を与えた

I'm gonna clobber you!!:
Stunned an enemy for the first time by attacking their weak point

You need to stun a boss by landing a combo on him when a yellow sign above their head appears and then hit him while he has those stars circling around above his head. 

 仲間ならいるさ! 
初めて仲間ストライクを出した 

You have a friend:
Performed your first Crew Strike.

When you're close to some of your allies a green beam may appear. Press  and on the left side of your screen a combo will appear. Execute the combo and you will swap with your ally. The trophy should unlock as soon as you've swapped with your ally. 

 おれは一人だ 道をあけろ!!!! 
初めて1エピソード内で1000人撃破を達成した

I'm by myself. Get out of my way!!!:
Defeated 1000 enemies in a Single Episode for the first time!

The fastest, easiest and safest way to get this is the Prologue in the Main Log. Just avoid executing the combos on the left side since it will avoid for the Pacifista (boss) to appear for a long time. You should get to 700 kills that way and then when the Pacafista appears just avoid killing him till you reach 1,000 kills. The downside of doing it this way however is that the prologue doesn’t give you any experience.

Another easy way to do this with earning experience is on Zoro's last level in Another Log. Just capture all fields and then let opposite captains recapture your fields until you reach 1,000 kills. Just in case be sure to keep a watch on the health of your allies. 

 あ~まいった　力　入らねぇ 
海などに10回落ちた

I Feel All Weak...:
Fall into the water or off platforms 10 times. 

Only possible in the Main Log. At times Luffy needs to jump or swing around by the use of . Just intentionally let yourself drop down 10x during it. Also you don't have to especially fall into water nor does all 10 have to happen in the same level so you can spread it out if you're worried about your health or if you're not a hurry you can always wait for it to pop by itself. 

 わりぃ　おれ死んだ 
エピソードを再挑戦した

Sorry, I'm a goner:
Retried an episode. 

Pretty self-explanatory. Just let yourself die and retry the level. 

 おせぇ 
パシフィスタへの特別な攻撃に成功した

Too slow...:
Successfully performed an event attack on a Pacifista.

Only possible in the prologue of the main log at the end of the stage when you face of against a Pacifista.

When he has one bar left you need to stun him. After he is stunned (when stars appear circling around above his head) an  sign above his head will also appear. Get close to him and press  then  + , hold  + , ,  repeatedly and finish it of with  .

You can stun an enemy by landing a combo when he has that yellow sign above his head. You could also equip the coin combo: Mr 2, Magellan, Transponder Snail which increases the chance to stun enemies: