2. Possibly a maximally great being exists. (Premise)
3. Therefore, possibly it is necessarily true that an omniscient, omnipotent and perfectly good being exists (By 1 and 2)
4. Therefore, it is necessarily true that an omniscient, omnipotent and perfectly good being exists. (By 3 and S5)
5. Therefore, an omniscient, omnipotent and perfectly good being exists. (By 4 and since necessarily true propositions are true.)
The contentious premise is 2 and the contentious inferential move is the S5 axiom (possibly necessary implies necessary). Parodies of reasoning along the lines of a so-called "Invisible Pink Unicorn" or "Flying Spaghetti Monster" can be dismissed as violations of premise 2, that is, they aren't even possible; this can be determined by their properties other than supposedly being necessary.
Premise 2 is contentious because of the argument from evil. According to this argument, a the existence of a maximally great being is inconsistent with the existence of evil. However, this can be countered by the so-called free will defense, that is, that a world in which there is free will is inherently better than a world without free will; therefore, a maximally great being would create a world in which there is free will and infringing upon it is something it refrains from doing, since it is omnibenevolent.
S5 is contentious because some logicians hold that S4 is the proper modal frame for necessity and possibility and "possibly necessary implies necessary" is neither an axiom nor theorem of S4, unlike S5. That is, in S4, the move above from 3 to 4 isn't valid. However, if S4 is taken to be the proper modal frame, one needs an underlying logic that doesn't presume classical negation (as that is also a result of S5, not S4), that is, one needs an intuitionistic logic that doesn't assert bivalency. Independently, this can be argued for by denying prelinearity, that is, that given any two arbitrary (even tototally unrelated) statements, one logically implies the other; one can deny prelinearity by pointing out a myriad of terms that are such that neither implies the other. For instance, that I am at my computer neither implies nor is implied by it being daytime at my location. One could argue that the proper way to conceive of implication is strictly, not materially, but the intuitionistic is free to argue that since his semantics for logical operators is grounded in their introduction rules (and conservatively extended by their elimination rules), that the modality of implication is inherent; that is, implication necessarily brings the meta-linguistic concept of valid inference into the object language: (S -> p) iff (S |- p), symbolically.
So, while one of the premises and one of the inferential moves are contentious, I agree with Plantinga that the above argument is "victorious" in his sense of the word, that is, it shows that belief in a maximally great being is not irrational.