the only real weakness Tirek showed when fully powered was Rainbow Power (which acted like an extremely potent variant of the Elements of Harmony).
Tirek, in his weakened state, required the aid of Discord to fully accomplish his tasks.
like any absorption-based entity most of Tirek's powers are stolen from other entities, meaning his base form is much weaker than what he achieves via said stolen abilities.
Tirek is arrogant, cruel and dependent on brutality to keep command - thus he is ill-equipped to deal with opponents powered by strong positive-energy or ideals (it also makes him under-estimate opponents).
Tirek, as it currently stands, is unable to escape Tartarus without aid - since it took him many years to formulate an escape the first time around.