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Since dealing damage to Anti-Matter increases the damage dealt by the antimatter pulses during the trial a league that attempts this badge will need solid healing support to counteract the fact that while attempting this badge the pulses will dealing 90% of all league members maximum HP in damage during the attempt. However, there are methods to reduce the impact this will have on the trial run.
When bringing Anti-Matter's HP below 10%, remember that he has no regeneration during the reactor phases, and so his health bar will drop faster than an archvillain's normally would.
In order to qualify for the badge, Anti-Matter's health must be reduced before completing the first reactor phase; however, this can be done just before activating the last terminal. The easiest way to clear the first reactor phase, therefore, is to power 9 of the 10 terminals, then reduce Anti-Matter to sub-10% health before powering the final terminal.
The increased damage from pulses due to low Anti-Matter HP only occurs while Anti-Matter is out during the reactor phases. The time between when the second and third reactor phases start and when Anti-Matter appears have only the normal pulse damage. The more productive the league is during that time, then, the less time must be spent dealing with the boosted pulses.
In the second reactor phase, reactor terminals are unlocked and can be freely powered before Anti-Matter arrives. By having all league members use damage-enhancing inspirations like Enrage and Ultimate, the Power Cell-carrying Goliath War Walkers can be defeated faster. By having league members who receive Power Cells use them to charge Reactor Terminals immediately instead of waiting for the league to collect enough Cells to charge the terminals all in one go, terminals can be fully charge before Anti-Matter arrives on the field. By using both strategies, most or even all of the terminals can be charged before Anti-Matter returns and the antimatter pulse is boosted.
In the third reactor phase, the countdown timer to Anti-Matter's return does not start until 10 Power Cells have been collected. This can be exploited to power most or all of the terminals before Anti-Matter returns. Open the doors to all of the bunkers containing Power Cells before grabbing any of the glowies, and be sure to clear out the WarWorks inside the bunkers as well. Position one or two league members in each bunker to grab cells. These league members should either be durable enough to run past the WarWorks without dying once they enough cells have been collected, or have enough stealth to sneak out unseen. They should also have strong enough self-healing or enough green inspirations to survive several antimatter pulses. Have all other members of the league begin clearing WarWorks guarding the terminals on the reactor.
The players in the bunkers should grab the glowies holding the cells at roughly the same time. Collecting all three glowies in all three bunkers will give a total of 18 Power Cells, starting the countdowns to Power Cell restocking and Anti-Matter's return. The Power Cells will restock before Anti-Matter's return, however, and grabbing all three glowies in all three bunkers a second time will give the league enough cells to power all ten reactor terminals. The players with cells can then proceed to charge terminals, with help from the players clearing WarWorks.