This story is really good in some aspects, and really quite bad in others.
For the good things:
The grammar and spelling is pretty much perfect, and scenes are written in a way that you can easily understand and visualise what's going on.
The premises and plot threads of each jump were really interesting (except for the pokemon world, which was rather bland, but even that had the cool idea of megastones being compared to evolution stones and being made permanent at the end). I mean, kicking the humans out of the far north and repopulating the giants, freeing Kurogiri from his mind control and becoming his apprentice, kidnapping Azula and swapping her role with Zuko's, all of these are top tier ideas. (I didn't read the Mass Effect arc since I never played the game and didn't see the point in powering through it since it was the last arc, anyway).
The background worlds are very consistent with the canons', and have reasonable and well thought out outcomes in relation to the butterflies of the mc.
There are lots of chapters, which is always a good thing.
For the bad things:
This gets better as the story goes on, but at the start the story is very very rushed. It feels more like the outline to the story rather than reading an actual story at times. This problem started to get better during the mha arc and was pretty much gone during the avatar arc, though.
The second problem, I think is related to the first. The mc has no personality. During the first arcs, everything was more like a summary of what the mc did without exploring his mindset while doing it, or showing his conversations with others. Then, because of this, when the quality started to improve, there was no personality to build off of so he turned out super boring. In the mha world, it's like he's acting professionally all the time. In the avatar world, it's a little better, but still pretty bad. Like, even though there's romance, it's more like "by the way, we're dating now" than any sort of flirting or blushing or exploring their feelings or, well, anything, really.
So, yeah. Good in some aspects and bad in others, but imo the good outweigh the bad and the bad slowly get better as the story goes on.