He will use a sniper rifle if you are distant and a machete if you are close to him. He has a close-in stabbing attack that the other hunters don't have.
The simplest strategy is to climb to his position, attack him with a fast weapon (the Spiked Bat, Driller, and Flaming Gloves are all good choices) and dodge his knife attacks with jumps.
Like the other hunters, he prefers to use his rifle, and will attempt to flee from Chuck so that he can engage with it. If Chuck follows him quickly, he can attack Earl while he is changing weapons, scoring several unanswered hits.
Chuck can use either a shotgun or an LMG to great effect, if you position Chuck at an intermediate distance from him and open fire. When Earl pulls out his machete, back away. When he pulls out his sniper rifle, move in closer. When he flees, follow him. Keep the gun centered on his chest and fire continuously. With precise timing, you can reduce Earl's health to zero, and he will be too busy changing weapons to actually do any damage to Chuck. It should take about 15 shotgun rounds, or 150 LMG ones.
Engaging Earl in distance combat is not recommended, his sniper rifle is accurate and powerful. Even if Chuck has maximum health, high-end healing items, and a sniper rifle of his own, he can expect to lose about 25-30 bars of health just to vanquish one hunter.
Hiding under him and using Power Guitar to attack him is also effective, and far safer since Chuck will not be in his line of fire.
Easiest tactic is to come with 2 bambows and sit just below and in front of Big Earl's position. From here shoot the exploding arrows in just above Big Earl. Immediately done for.