This isn't a complex pun, it's just a paragraph that builds incredulity for comic effect (although to be honest, it's not particularly funny).
The entire purpose of the whole paragraph is just a poorly written, badly formatted, and frankly not particularly funny description of something that is supposedly an "in joke" to the n-th degree.
The levels are thus:
Mr T is a cultural reference to the man shown below, who is most famous for his role as B.A. Baracus, in the American Cult TV show "The A-team" in the 1980s.
According to Wikipedia, this fictional character is described by a fictional reporter in the pilot show as:
Bosco Baracus. Known as B. A. for 'bad attitude.' The man is a mechanical genius. He also has one of the worst conduct records in the army. He likes to slug officers.
To get back to your original paragraph:
In the mental image, you have a brother, who supposedly likes being "ironic", and he owns a doll in the shape of Mr T.
The paragraph then goes on to try and say that the reason your brother has the Mr T doll is because it is a in joke of an in joke of an in joke.
At its most basic level, the in-joke is about Mr T, who was originally thought to be awesome (because of his portrayal in the A-team), but which you and your brother think is "lame".
But according to the speaker, this is not the reason your brother owns the doll. The in-joke that Mr T is "sort of lame" "might have been funny [...] eight years ago". No. The reason you have the Mr T doll is apparently much more clever and funny than simply a one-dimensional in-joke.
At the next level, the in-joke is the in-joke about Mr T itself. Mr T is "awesome and badass" because of the in-joke.
At the next level described by the speaker, the thing that is funny about Mr T isn't Mr T. It isn't the in-joke about Mr T being lame, and it isn't the in-joke that the doll is awesome because of the in-joke about Mr T being lame; the thing that is funny is the fact that the in-joke is so complicated and has so many levels.
In particular, the funny thing is how extremely convoluted the joke is, and consequently how difficult for people other than you and your brother to "get" the in-joke, making it apparently all the funnier. This is the meaning of the sentence "Only highly adept satirical ninjas like you and your BRO can appreciate stuff like this" in the paragraph.
But when we boil it all down, what we see is that everything after the words "It is" is really just a complicated and silly description of a three-level meta-joke that is very ironic, with an example centering on a Mr T doll.