The quickest way to level up one character to level 5 is to play the mission called "How to Live in This Ocean"
you can find it under the Treasure Log the East Blue.
Really easy mission just have to get a set amount of Berries. Your group has to reach 2000,000,000 Berries to beat the mission. you can play solo or up to 4 people. I found the fastest way to complete this mission was to stand next a spawn barrel and keep defeating the enemy as the spawn. The more you defeat the more points you get at the end of the game. Playing this way you can gain 2 levels each run.