What is the expiation for failing to fulfill a pledge to Allah Almighty three times, knowing that one of those times was a prayer in which he strove, and that he gave charity for the first two times?

If what transpired from you was merely a promise (saying, "I promise Allah such-and-such"), then nothing is incumbent upon you, and it is not considered an oath or a vow; however, it is recommended to fulfill it.

As for it being a covenant (saying, "I covenant with Allah such-and-such"), there is a difference of opinion among scholars regarding it. If the covenant is considered an oath and you broke it three times, then you owe three expiations for an oath. These are: feeding ten poor persons, or clothing them, or freeing a slave. If you cannot find any of these, then fasting for three days. You must do this for each time you broke the covenant.