Alan Rickman did not receive an Oscar nomination for portraying Hans Gruber in Die Hard.
Alan Rickman portrays the head "terrorist" Hans Gruber who invade the building and take hostages. Something I should note right away is that Rickman honestly tries very little to be an east German. He sort of does an accent at times but usually leaves as soon as it comes in his portrayal. Also in any of the times he appears to speaking German it is in fact Germanesque gibberish from him. All this really does not matter, and what might seem a flaw in a different performance only honestly adds to the fun of the performance. Rickman knows he is playing the villain, just as Christopher Lloyd did in Roger Rabbit, and play up that fact for all that it is worth.
I think the best word to describe Rickman's performance here is delicious actually. He takes such a delicious method with material, and plays the part of Hans as deliciously evil. There is not any doubt in Rickman's performance that Hans is just no good, and he has a lot of fun with playing up that fact. Rickman is brilliant here because he does not overact the role to the point of being unrealistic but instead he takes just the right amount of flamboyance with his portrayal. Rickman is entertaining as possible really as Gruber comes in and takes over he building with his unique style and precision. Rickman effectively makes Gruber both an imposing villain as well just an entertaining character.
As a more straight up villain Rickman actually infuses them equally with his scenes of gleeful fun as he makes that as really part of the danger of Hans as the violence comes from him so easily without any hesitations. Rickman is quite good because he really does not show any sadism within his performance or anything such as that instead he is quite chilling by being so matter of fact when he kills. Rickman shows Hans takes a very up front method to the proceedings. For example when he commits his murders in the film he makes Hans slightly bemused not really exactly getting joy out of the killings but rather getting the joy out of getting rid of someone he was frankly just tired of speaking to.
As Gruber Rickman is the proper threat against John McClain as Rickman makes Gruber a man of cold calculation who use all that he has to get through his plan. He makes him very believable in the way Gruber adapts to the new challenges presented by McClain and the cops who eventually appear on the outside. He is particularly great in the scene where he accidentally gets caught by McClain and is able to talk himself out of it by pretending to be a worker who happened to get lost. He could not be better in the scene as he goes from one second with his evil calculating stare, to the next with a believable yet phony fear along with a believable yet phony accent as he tricks McClain into thinking he is a hostage.
Rickman is terrific in the manner in which he makes Hans very much a cunning intelligent business like villain, and within this context is where Rickman is able to make what is so entertaining about him which is in the little thing. Rickman makes the little asides in his performance so very enjoyable. Whether it is the way he comments on the way he also has two of the suits the businessman he soon to murder has in such a casual manner, to the way he casually says he read about one of his supposed terrorist comrade groups in Time magazine, to his conversations about westerns with John McClain over the radio, he is terrifically entertaining in the way he gives Hans just the perfect style and wit.
Rickman enlivens the whole film which frankly could have become excessively gruesome if it were not for his take on the part of the lead villain. Even when he is being awfully dark in certain scene in the menace he creates through the incisive fashion he works through every scene and every part of his plan he lightens all up with that clever little style that even when we are against him Rickman some how still let us enjoy parts of his plan through his unique humorous fashion he takes with the part. He is able to balance the elements of Hans perfectly with the part as he makes it an easy film to watch him try to get through his plan. He is a great adversary in the film, and just maybe the greatest in any action film ever. Hans Gruber could have been a throwaway baddie but Rickman makes him one of the most memorable through his brilliant use of a certain class and dignity in such an undignified character.