Let's b-b-break it down.
Okay, first off, the background starts out quite bright, suggesting this isn't actually the start of the transition, although it is the start of this .GIF. Anyway you can create a brighter version of an image with an appropriate matrix, such as
im.matrix.brightness and dissolve to it. That part is easy.
Now, the image fades to a darker version and then to black-
im.matrix.brightness is suitable here too. However, that effect with the background being pushed off to the side in a randomly staggered fashion is not something ren'py can do. You might be able to fake a similar effect by having multiple
CropMove transitions and some complicated mess of
AlphaDissolves but you would never get it exactly. It's an ugly effect in most situations and this is one of the few examples where it actually looks decent, so it's not a huge loss that this isn't in ren'py. You could manage something that looks about as good with a fade to a darker version of the background coupled with an
ImageDissolve (using noise as the control image) and
slideawayleft or something like that, probably. Either way, the screen goes black by the end of this portion.
Here, the sprite, white and with progressively darker shadows trailing slides in from the left. It's very easy to make a sprite completely white. You can use
im.matrix.brightness again with a value of 1. For a live approach, you could use
AlphaBlend (control=the sprite, old='#0000', new='#FFF', alpha=True), or you could just have a completely white version of the sprite, whatever. Now, you need to animate that sprite coming in. I'd actually recommend creating a new layer or something to do this on so that you can do it while other transitions are happening behind it, because some more transitions are coming up. In fact, I wouldn't do this specific part with a transition at all. Moving a sprite across the screen is the easiest thing ever with
ATL. Now, there isn't just one sprite here, there's 5 of them. The darker versions are actually slightly bluer than the main sprite. Up to you if that's important or not. Now, at first I couldn't tell if the other versions were simply darker or were more transparent, but no, they're darker and fully opaque - this is because the brighter ones cover the darker ones entirely and there is no blending taking place. Creating darker version of the white form of the sprite is again easy- you could blend with the right colours, use another matrix, whatever. Just give them ATL as well and have them move in from off the screen to the final position, each one progressively offset to the left. Remember to 'show' the darker ones first so the lighter ones end up on top. Next, all but the brightest one need to fade away quickly after reaching the final position- alpha isn't really appropriate here, but could do in a pinch.

Here, the white form of the sprite fades into the standard form. Here transitions start happening behind it, so it's a good thing we're working on a separate layer. You could either do this by showing the coloured form of the sprite over the white form and just having it fade in, then vanishing the white form really quick. This can sometimes cause issues with the partially-transparent antialiasing pixels at the edge of the sprite though, which will be less transparent (and therefore look different)- this could potentially be fixed by making the white form of the sprite slightly larger than the standard form. Alternatively you could use
AlphaBlend here too, with 'control' being an ATL image fading from fully transparent to fully opaque, old being the white form of the sprite and new being the coloured form. There's a few possible solutions, actually.
Now, behind it. the background is fading back in, again to a darker form (so
im.matrix.brightness again) with black bars on the top and bottom- this could just be one image drawn on top of the background. There's also a line scrolling in - for now, let's just make that line a sprite and ATL to bring it across.
The sprite is still fading from white and the background is still fading in, but we have another effect, the 'Sword Blitz' text appearing. This is another transition, and a simple one- it's just
ImageDissolve with bars of random brightness. Too easy. It might need to happen on a separate layer, but that's not a big deal- note that it's not necessary to use separate layers for all these things, it just simplifies certain things somewhat.
Here, the subtitle or description or whatever comes in, appearing left to right. Also too easy. I believe this is the
wiperight transition (you can do this with
CropMove to get better control over speed etc.)
Now, we fade everything in to the original background again. The transition used here is obvious- it's
ImageDissolve, but I'm not precisely sure what the control image used is. It appears to be two sets of blinds, one a vertically flipped version of the other, on top of each other, but this is something you'd play around with.