Did Hiro rebuild Baymax all by himself?

He didn't just learn all that robotics in a few months. When we're introduced to Hiro, we see that he already is a robotics genius. We see that he built his little fighting robot that can take on other fighting robots seemingly built by "professionals".

Later, he invents and builds the builder bots that can shape shift in to any shape he needs, and he can control them with his mind. This is considered an astonishing achievement even in the highly advanced technical world of Big Hero 6.

As a side note, the robots fighting scene at the beginning of the movie is also an indication that robots are so common and easy in this society that criminals can easily build them for illegal fighting pits.

So to rebuild Baymax, we see that he already had the know-how to build the body. He just needed the brain. That was where the chip came in handy.

Another thing to consider is this: Hiro has already inspected/modified Baymax on 3 separate occasions on-screen. These are simply the instances we've seen, some of which are abbreviated for the viewers since those scenes in real time would likely be extremely long and boring.

1. Hiro does an up-close inspection of Baymax when Tadashi shows him around his university robotics lab. Hiro even recognizies a large chunk of the overall parts/design choices with Tadashi only occasionally correcting him.
2. Hiro performs modifications to Baymax by designing and fitting carbon fiber body armor, and reprogramming him to know martial arts. Presumably, Hiro also includes his "kill mode" AI override at this time.
3. Hiro performs a second round of modifications with more robust armor, rocket-powered fists that Baymax can intuitively control, and rocket powered feet that Baymax can intuitively use to fly.

It's safe to say that Hiro is already pretty familiar with how Baymax is constructed/designed. As other answers point out, he's already extremely familiar with many advanced robotics concepts. Considering Hiro's intelligence, knowledge of robotics, and intimate familiarity with Baymax's construction, it's pretty easy to conclude that Hiro could reconstruct Baymax (compared to the time/effort Tadashi spent on the original design at least) in a short amount of time.

The hardest thing to replace is probably Baymax's AI. (DISCLAIMER: the movie implies that the AI code was critical and nearly irreplaceable when Hiro discovers the AI chip in Baymax's rocket fist. But... source control and data backups are presumably still things that are utilized in the future, which would otherwise invalidate all of this.) Baymax's physical characteristics, with the exception of his medical sensor, isn't a huge stretch of the imagination compared to what we're capable of today. But programing complex AI's today is already the most complicated and time consuming part of building a robot and Baymax's AI is incredibly more advanced than anything we're capable of creating. It is likely the single most complicated part of Baymax's entire design. Hiro likely could recreate it, if necessary, particularly since he built a more simple and singular AI mode into the martial arts chip he created for Baymax. But, it's doubtful he'd get every single detail in Baymax's personality and responses exactly the same way Tadashi did, and all of the data for the experiences Baymax had would be lost.

As already pointed out by DeeV, Hiro is no newcomer to robotics. However he has a headstart rebuilding Baymax in that his brother has already done all the heavy lifting in terms of designing Baymax, and overcoming any design issues. He has probably also kept some level of documentation of his progress. Hiro just needs to find any schematics, parts lists, etc. that his brother kept when building the original. Not to mention Hiro has probably already spent some time tinkering, and may already be quite familiar with the design.

No way Tadashi didn't keep detailed plans, designs, schematics, notes, spare parts, earlier versions, prototypes of various pieces, etc.

Hiro would certainly have not been building Baymax 2.0 from scratch.