In which way do the engravings represent Dean Corso's journey towards The Ninth Gate?

I will provide you with two links in following paragraphs that should give you sufficient insight into the engravings and how the movie incorporated them.

It is important to keep in mind that we're talking about a psychological film here. Esotericism is central to the entire plot. That's why it's vital to understand that the engravings are not meant literal. I'm sure you know that duality is a (if not THE) main theme in this movie. So that literal vs. psychological/philosophical aspect of the engravings also plays into that. Spoiler alert: it's not the literal interpretation that will grant you access to enlightenment/the 9th gate. The only literal link I would draw is a physical resemblence between movie characters/actors and the people in the engravings.

An interesting analysis compared the interpretations of Balkan, the Baroness, and made an additional link between the engravings and Tarot cards. And in a surprisingly concise manner. You can find that here:

The nine engravings in the film are a little different from those in the book, in one way. The faces of the people in the engravings physically resemble the characters who appear in the film around the same time we see the engravings. In that same vein, in image 8, instead of a sword, there is a club, wielded by a man who looks like Balkan. The effect is often rather humorous, even when Corso gets hit over the head. For the ninth image, Balkan has identified the castle in the background as a particular one he has purchased...

Balkan sees the sentence as applying to himself: he has traveled in silence by a long and circuitous route, sparing no expense, etc. He overlooks the possibility that it might apply to Corso, who does the actual legwork for Balkan. In the film, the faces in the drawings resemble those of the people that Corso meets, and the scenes correspond to what Corso experiences. One face even looks like Corso himself, or rather the actor Johnny Depp, who plays Corso.

The different “gates” then seem to be different tests that allow one entrance to something, if one able to manage a long and circuitous route, brave the arrows of misfortune, etc. It is Corso who does all these things. Yet it is none too clear from Balkan's interpretations what one is entering into. It is simply “the ninth gate,” the gate to a burning castle. Balkan assumes that he is being admitted to a pact with the devil, one that gives him supernatural powers, but there is nothing in his interpretation of the drawings that implies this, apart from the letters LF. It is only legend that associates Lucifer to pacts with the devil giving vast power. In Latin the word “Lucifer” means “light bearer.” The film, at the end, suggests that the successful initiate enters a world of light, corresponding to the meaning of the word. Perhaps “light” is a metaphor for hidden knowledge that the various trials enable an initiate to have. Whether this knowledge implies any power on the earthly plane is unclear.

Another blogger (though that term doesn't do justice to the level of analysis done in his 'essay') was made by D.J. Rodger and can be found here. He goes into each engraving and makes links with interpretations from Tarot as well as myths and legends. Connections for (most) interpretations are made with regards to Balkan and Corso in the movie:

This is a story of duality. There are two journey’s occurring here. One is Boris Balkan: fervently materialistic, hungry for acquisition and determined to go after what he wants. The second journey is that of Corso; through the narrative of the story he becomes a seeker of knowledge without any clear vision of what the outcome will be. Both men are travelling in opposite directions. One is heading towards ultimate destruction, dragged down into the fires of Hell, to become lost within the Kingdom of Shadows; the other is heading towards Enlightenment, to claim a prize he never knew existed until the moment of final revelation. Neither man is innocent, but one has failed to “play by the rules” and so suffers the integral trap contained within the riddle of the book and the engravings...

...Additional complexity can be added by stating the protagonist is required to enact all of the scenes portrayed within the engravings. It’s certainly not included in the film, and although a feasible and interesting concept beyond the constraints of a tight script, I don’t think this is suitable for the game that is afoot. It places far too much literal interpretation of the engravings. And this story is more about the spiritual and psychology interpretation...

...Each of the nine engravings represents a particular life experience, generic or specific, that one must go through in order to gain access to the world of Light and Illumination. Acquiring the engravings was merely a part of that journey; defining the map, so to speak.

The first blog (possibly in combination of the second one) should probably quench your thirst for the link between the engravings and the movie. So again, in short: no, it's not literal (apart from perhaps certain physical similarities of movie characters/actors and the people in the engravings). It's all philosophical/psychological.

But if you can't get enough....

Finally, here's an academia.edu link that goes into the details of the symbolism of the movie. At length... so if you're short for time, this is not the read for you. Note that this also covers the engravings, but is not limited to them. It focuses heavily on a qabalistic/religious approach though. But then again... considering the movie we're talking about, it's not that far fetched to use a religious basis to build the analysis on.