(To understand the context of this battle, it helps to refer to ERB #2, which also featured Vader and Hitler. In that previous battle, Vader had Hitler frozen in carbonite. The case was presumably escorted to Jabba the Hutt's lair, where this battle opens with a masked character (Boushh) disengaging the case locks and thawing Hitler out.)
(The same line and situation is a parody of the scene in "Star Wars Episode VI: Return of the Jedi", when Han Solo is thawed out by Leia Organa. After being frozen for so long and then thawed out, he is blinded temporarily and she is in disguise, so he asks who she is. Someone is in the same disguise Leia wore, and Hitler is also partially blind as he is unfrozen after over a year of being trapped in carbonite. He asks who saved him, but he doesn't get an answer until he is picked up by the arms of...)
Someone who loathes you, bitch! Now stand up and rhyme!
(Vader is referring to a line from the above scene. When Solo asked who his rescuer was, Leia replied, "Someone who loves you." Here, Vader tells Hitler it's someone who loathes him, which is basically a lot of people since Hitler is one of the most evil and most hated people in history, but Vader hates him a lot more because of how they've battled each other previously. He just wants him to stand up and begin rapping.)
I only thawed you out so I could beat your ass a second time!
(Vader only wants a rematch against Hitler just to diss him once more. He's confident that he can win again, since he won, based on the polls in ERB #2.)
Roar like Chewbacca! The voice of Mufasa!
(Vader's voice actor, James Earl Jones, has a deep, booming voice that would make a fine roar, like that of the famed Wookiee, Chewbacca. Jones also did the voice of Mufasa in "The Lion King".)
I'm on the leader of your limp-dicked Luftwaffe!
(The Luftwaffe is the German Air Force. Vader says here that he's ready to shoot down what he thinks is a weak, easy target. In "Episode IV: A New Hope", Vader tailed Luke Skywalker in an effort to defend the Death Star from the Rebel assault. When he reported to control, Vader said, "I'm on the leader.")
I strike back hard against a Nazi!
(A reference to the title of "Episode V: The Empire Strikes Back". Vader claims he can hit Nazis like Hitler where it hurts with his rapping.)
Brain-toss your ass in the air, Yahtzee!
(The brain toss is a Force power. Vader thinks he can throw Hitler around using his mind, and when Hitler lands, it'll be the perfect throw. In the game of Yahtzee, the perfect throw that gives the game its name has all five dice with the same number facing up. A player is to call "Yahtzee!" when this happens.)
Ask Indiana Jones who the fuck I am.
(Vader references "Indiana Jones", the other major film franchise made by George Lucas after "Star Wars". The plot of "Indiana Jones and the Last Crusade" involves a resurrected Hitler in the race for the Holy Grail against Indy and his motley crew. Since Lucas was behind both sagas, Vader assumes that Indy knows him personally and would tell Hitler about him if asked. He's giving off a sarcastic "What, you didn't know?" Indy also asked for Hitler's autograph in the movie, which caused Hitler's plans to become foiled in the movie. Indiana Jones was also played by Harrison Ford, who is Han Solo in the Star Wars trilogy. Like Hitler, Han Solo was frozen in carbonite by Vader as well.)
I spit sick shit so focused, I break your concentration camp!
(Vader believes that his rapping is as good as his control of the Force, and that it is powerful enough to level one of Hitler's death camps. A subtle pun, as "to break one's concentration" is to make that person lose focus on whatever he's focused on, which ties in with his use of Hitler's concentration camps, his main way of killing Jews and other groups during World War II.)
I'm a certified Sith Lord, you runt!
(Vader attained the highest rank in the Order of the Sith, so he says he can outrank Hitler. He calls him a runt to demonstrate he has higher power, as Hitler was also considered to be smaller than average size.)
So suck on deez!
(Vader's used this line before, so the viewer should know what's next.)
(Stormtroopers often asked Darth Vader to repeat himself or confirm what he said in order to avoid making a mistake, because mistakes were usually punished with death.)
Deez robot nuts!
(Referencing a line he had in their first battle, Vader once again tells Hitler, "Suck my robot balls.")
I'm gonna enjoy watching you die.
(He's going to enjoy seeing the death of Hitler after he destroys him in this battle.)
So let me do it with my own eyes!
(In fact, he'll want to see it happen with his real eyes, as opposed to seeing it with his helmet on. This is also a reference to a line in "Episode VI: Return of the Jedi", where he asked Luke, "Let me look on you with my own eyes.")
You look stressed, Vader! You appear to be in pain!
(The style in which Hitler says this is reminiscent of Hitler's line from the previous battle, "You stink, Vader! Your style smells something sour!" Taking the helmet off without proper pressurization has caused Vader to stress out, as this is painful for him due to the extent of his injuries. Hitler can sense this in Vader's body language.)
You need a vacation. Here, take a trip on my train!
(Another throwback verse, with the original being "You need to wash up, dawg. Here, step in my shower!" When a person is as stressed as Vader, he usually takes a vacation. Hitler invites Vader travel on his train, which normally rounded up Jews during the Holocaust, thinking they were being sent to a better place, when in reality, they were being sent to one of his infamous death camps.)
I mean you? Leading an army of white men? Disgraceful!
(Darth Vader is leading an army of Stormtroopers, who wear white armor, while Vader commands them with his entirely black suit. Hitler thinks that the white males are the dominant species, which is why he finds a darker person being in charge of a group of white figures to be offensive.)
Even your mic skills still aren't fully operational!
(The Death Star, Darth Vader's massive space station used to destroy planets, was blown up, and Vader had to rebuild a second Death Star. While it was being constructed, it had turned out to have, once again, a small weak point that could blow it up. The Death Star's construction workers often reassured Lord Vader by telling him it was "fully functioning and operational", but when it was destroyed again in the last Star Wars movie, it had never actually become fully operational. Due to the compromises made in creating Vader's armor, he can't breathe or speak as well as other men. Hitler mocks his rhyming skills by saying they're not fully operational like the Death Star. In other words, he cannot operate his raps as well as Hitler can on the mic.)
You got one bitch pregnant then gave in to the hate.
(Anakin Skywalker had a secret affair with Padmé Naberrie prior to his turn as Vader, by which he bore twins Luke Skywalker and Leia Organa, but in rage over his defeat by Obi-Wan Kenobi, he inadvertently Force-choked Padmé, killing her and accelerating his descent toward the Dark Side.)
Now you're 6'6" and black but can't get a date!
(Even though Vader is tall and clad in black, Hitler says Vader's not picking up women in that life-support suit, despite a tall dark male usually being a good catch for ladies.)
Lightsaber? You need a Life Saver!
(Hitler is saying here that Vader's lightsaber, the weapon commonly used by Jedis and Sith in Star Wars, will be no aid to him in this battle, and that he will need a something more to save his life, as the fact that he's barely alive in his suit makes him almost dead. A Life Saver is a ring-shaped candy in either mint or fruit flavors made by Wrigley (and it sounds like lightsaber). Hitler is saying Vader needs to suck a mint Life Saver to freshen his breath, as to him, it stinks..)
Use some of your Force to fix your fucking respirator!
(Vader uses a respirator to breathe, since he was severely damaged after he fell in lava after his fight with Obi-Wan Kenobi. Hitler says if he's so powerful, why doesn't he use his Force to make his respirator work properly?)
You think you're powerful with your finger neck pinches?
(Darth Vader uses finger pinches to choke his enemies with the Force. Hitler finds it dumb that his intimidation came from something so lame as finger pinching.)
You couldn't even get your own son into the family business!
(This is referring to the fact that Darth Vader’s son, Luke Skywalker, was opposed to him, rather than with him. He tried to get him to join the Dark Side so they could rule the galaxy together, but he couldn't get him to do so.)
Everything you do is an epic fail!
(Vader's plans had normally ended in an unsuccessful attempt: building the Death Star, getting Luke to join him, fighting Obi-Wan, saving his wife, etc.)
Now stand at attention and Sieg fucking Heil!
(The phrase "Sieg Heil" was commonly used by German military during WWII; it basically means "Hail Victory" and was supposed to express that Hitler, who was commonly saluted with "Heil Hitler", was equal to victory. He suggests Vader ought to be doing the same to him.)
What's wrong Ani? Can't take any more?
(In the first Star Wars movie, Anakin's mother asks, "What's wrong, Ani?" Hitler thinks he dissed Vader enough and he boasts on how he is unable to withstand him any longer. It could also be a reference to how 'Ani' sounds very feminine, thus mocking Vader's manhood.)
Not surprising coming from the Emperor's whore!
(Emperor Palpatine is the real villain who controls Darth Vader, so Hitler thinks Vader is just his puppet, and he has to do everything the Emperor says. He's not surprised that Vader can't handle any more since he's basically the Emperor's bitch. Another interesting fact is that Emperor Palpatine and Darth Vader are both based on Hitler and Himmler, Hitler's second-in-command, so Hitler knows how much he's bossed around. Alternatively, Hitler could be saying that Palpatine and Vader have a homosexual relationship, which were illegal during the Nazi regime.)
Yeah! Ja, take zat! What's ze matter? Where is ze DJ? Why are you laughing?
(The music stops, and Vader starts laughing. This line isn't subtitled. Hitler proceeds for a moment but gets confused.)
(Vader had set Hitler up for a trap, similar to how he froze him in carbonite, and Hitler falls into the Rancor Pit, a trap used on Luke Skywalker in "Return of the Jedi". Jabba uses this to have trespassers fed to the Rancor, the monster residing in it. Now Hitler suffers the fate of possibly being eaten by the Rancor.)
(Hitler falls into the Rancor Pit, yelling "I AM ADOLF HITLER" as he does, repeating his first line from the first Vader vs Hitler battle.)