Trial of the Grand Crusader (this is a use name, not the actual name of the raid zone) is the heroic mode version of Trial of the Crusader. These are the hardest raid encounters before Icecrown Citadel.
A major difference between Trial of the Crusader and Trial of the Grand Crusader is the Argent Crusade Tribute Chest. Upon entering the Coliseum in heroic mode you will be given 50 attempts to complete the instance. If the raid wipes 50 times, all undefeated bosses will despawn for the remainder of the lockout period. A minimum of 25 attempts remaining is required for the chest to appear after defeating Anub'arak. Higher amounts of remaining attempts will reward more and better items and achievements.
In the Trial of the Grand Crusader, reach a Tribute Chest with 50 attempts remaining and without allowing any raid member to die during any of the boss encounters in 25-player mode.