All strawhat strategies are successful. This one is rather vague but not too hard to figure out. The most difficult portion is early on. Your goal is to get Ceasar Clown to the drop point, but also prevent Bellamy's group from taking advantage while your're gone. So take care of the mission-based captains in the town, all the while spending a bit of time supporting Law. All 4 captains in town must be defeated before Bellamy appears, and he must be defeated before he retreats. If you succeed, you will get a green "objective success" message jsut before Doflamingo appears. If not, you will get a red "objective failed" message instead.
A few other actions that may affect this Dressrosa mission:
- Going into the collosseum with Law
- Preventing all allies from retreating (against their will). This includes Bellamy who appears aftter - Fujitora & Doflamingo appear on Green Bit
- Preventing the Blackbeard captains from taking the territory to the south
- When Kuzan becomes a support, use him to destroy all underground entranceways (they look like phone booths) marked with a (!).
- Help conquer the Smile Factory before beating Fujitora and Kizaru
- Conquer the Territory where Fujitora starts
- Conquer the Territory where Burgess starts
- Conquer the Territory where Blackbeard starts
- When Bellamy returns as an ally, make sure he doesn't get defeated early on
- When facing Doflamingo (final boss), make sure to deliver the finishing blow on the real Mingo, not the puppets.
Note: I did almost everything of that and it worked fine. I believe that you must follow the instruction and complete all the tasks that will appear in bottom right corner. Don't forget to capture Toy Factory before Colosseum and to destroy all the phone booths with Kuzan. Remember - saves are your friends.