Bakugan: Defenders of the Core

To upgrade a Bakugan, choose a Bakugan on the partner select screen before a story battle. You'll have the opportunity to spend core energy like currency on upgrades to your Bakugan. When every upgrade for every Bakugan is purchased, the trophy pops.

Do not grind for this trophy until you have done everything else. Every battle you complete nets core energy. You have to run through story mode twice and then replay levels until you have an S rank on all of them. Those are all opportunities for a lot of core energy needed for upgrades. Upgrades and core energy carry over to all playthroughs.

Even if you save upgrade grinding for last, it will still take you a long time. Hours. You get the most core energy from beating the last boss over and over again in the Interspace. As far as I know, this is the most efficient way to get core energy.