So a couple of questions, so we can be clear.

1) Who is “the media” exactly?

All generally mainstream news outlets that are against Trump (i.e. WaPo, Vox, Salon, Slate, CNN, MSNBC)

2) What exactly have the accused parties done that was wrong or beyond their job description of reporting on Trump’s actions?

I believe this liberal professor addresses it well here: http://fullmeasure.news/news/politics/the-media-and-trump

I would also like to add that you dont need to be wrong to be an enemy. MMA fighters are enemies in the ring but neither are wrong. Trump and the media can be enemies even when the media is right.

3) What does the media have to gain by “attacking” Trump? What is their stake in this fight?

It's a mix. Capitalism and the need for "ratings" is one part. The relationship with the DNC is another part (look how interconnected they are by marriage for example). And their owner's personal bias is another. The WaPo loses money every month, but Bezos bought it to use as a weapon.

4) Considering that the media is subject to market forces such as supply and demand, why can’t it be the case that “the media” is doesn’t let Trump off the hook with embarrassing or negative stories because their invested parties (the American people) want to know this kind of information? Wouldn’t significant media “bias” simply be a result of the majority of media consumers not being interested in Trump apologetics?

Hard to parse what you're getting at, but let me reiterate- the media doesnt need to be doing anything "wrong" to be Trump's greatest enemy.