This is one of the last trophies you'll end up getting, next to the 100% Gallery trophy, as it requires you to grind through levels as specific characters, or with specific Crew characters, to raise their Crew level to MAX. This is the fifth level and is similar to a previous system in Pirate Warriors 2 or the Gundam Dynasty Warriors series (with friendship levels). A bit of helpful advice for raising the Crew Level:
1) Play as the different characters you can to raise them. This will help you with a decent amount, probably dropping about half of the required you need total and easily setting you up to get this trophy. This will also be needed for the skills you'll come to require.
2) Specific stages in Dream Log cycle through specific groupings of crew members. One found early on to the right is Fishmen vs. Giants, which is helpful for getting Hody and Arlong as Crew members. *
3) If you are going for a specific character in your Crew to raise compared to another (you've got Arlong and Jimbei, but you've maxed Jimbei), switch to the one you want and keep using that for Kizuna Rush/Attacks. I at least know that this will give you an increase in coins for this character as opposed to the other (Get Coins +2, +4, +6, +8 for Arlong whereas you might not even get +2 for Jimbei). Along with the played character getting the full use of the Beat ("!") experience, the more often you've got specific characters in your Kizuna Rush, the more experience they will get too.
As noted, you'll end up raising every character up to MAX in the long run, so this is just a simple step in the long run that requires a lot of effort.
*EDIT: Someone has compiled a Google Doc spreadsheet with options on which islands to use to help with raising the bond of specific non-playable characters. They have gone above and beyond to provide the info, so special thanks to them for that. However, they have since attempted to dispose of the information. I have salvaged it and have posted it back up:
https://docs.google.com/spreadsheets/d/1Ft0nungVMJCACTOFSiuP...