Episode 1: Adventure on the Archipelago of Dancing Soap Bubbles
1. Use Nami to defeat all the Marine Captains within the time limit.
You must play as Nami in order to trigger this event. Near the beginning of the level, some Marine Captains will appear. Just defeat them quickly in order to trigger this event.
2. Defeat Kizaru and Sentomaru before they rendezvous.
As you go through the level, Sentomaru will eventually appear. You will be tasked with defeating him, but shortly after that, Kizaru will appear. Kizaru will start making his way toward Sentomaru. In order to trigger this event, you must defeat Sentomaru and Kizaru before they can meet up. This should not be difficult as Kizaru is quite a distance away and gives you plenty of time to fight Sentomaru.
3. Help Law's strategy succeed within the time limit.
As you attempt to retreat with your crew to the Thousand Sunny, some Pacifistas will appear and block your escape. Shortly after that, Trafalgar Law will appear and tell you about a strategy to easily get rid of the Pacifistas. On your map, you should see a light box that covers a bit of territory. Your goal is to lure the Pacifistas into this area and defeat them. If you defeat the Pacifistas in this area, Law will use his Chambres technique to transport them. Make sure you lure the Pacifistas well inside the area before you down them. Don't take too long because you are timed.