The phrase is correct as it is.
You are right that bei requires dative case. Since the noun Treffer is masculine and singular, the adjectives describing this noun needs to get the singular, masculine, dative ending as well.
Furthermore, there is no article-like word preceding the adjectives. Thus, we need to take strong inflexion (in contrast to the weak inflexion in bei dem ausgeteilten kritischen Treffer).
Thus, we end up with ausgeteiltem.
How can we know that Treffer is singular here, since the plural is die Treffer? We can tell, because plural dative would be den Treffern.
And why isn't it kritischem? Well, that is debatable. Usually, you use the same inflexion for multiple adjectives in a row (this is called Parallelflexion). Applying this, one could write bei ausgeteiltem kritischem Treffer.
However, it is possible to signal subordination of one adjective by using weak inflexion (this is called Wechselflexion, see the accepted answer for this question for example). This is, what happened here: there wouldn't be a critical hit, if there wasn't an allotted hit. Thus, it is correct to write bei ausgeteiltem kritischen Treffer.