The short version is likely to be artistic skill combined with some light hacking skills.
Longer version. First that search everything you reasonably can to see if there is an existing high res version of the model and any related textures out there -- remakes, other region releases, cutscenes, demo sections (if I wanted high res Mario 64 model I would get the face pulling thing at the start for instance), CGI films, advertising, leaks, base textures*, guest appearances in other games...
Hopefully one of those is better than the baseline but if you only have what is in the game then so it goes. Jazz Jackrabbit is one of the things that did not make the leap to 3d very well and has languished ever since (give or take the GBA version there has not really been anything since).
One of said later appearances, apparently there was a thing in fortnite as well but that looks like an in game poster rather than anything useful
Import this (and maybe several if there are multiple options you want to merge) into a more conventional 3d model editor however you will. This tends to be within the realms of ROM hacking as you have to figure out the format, though maybe you get lucky and find someone has already built such a thing.
So now you have whatever low poly count model was used in your editor. Might want to get whatever sprite work and print advertising of the 2d stuff also available as a reference.
Magic make it look better button is not yet a thing (AI just about does 2d images these days). Certainly try obvious things like the subsurf (turns what is nominally a few points on a line into more points but splitting the difference) to see what comes up there but you are likely to be sculpting a lot of things. Same for textures which is where the 2d and other reference material will likely really shine.
This is also where artistic talent comes in -- realism vs artistry is ever the fun discussion in these sorts of things, especially for a comedic animated character.
https://upload.wikimedia.org/wikipedia/en/a/a6/Lemming_animation.gif is 2d very small spritework but illustrative of what some comparatively small changes make.
You now get to export it to something the game uses, possibly not without first having to rig animations (I don't know what your host game uses on the mesh vs bones front and what its general ordering and pivot point list looks like, as well as distances between them (though Jazz Jackrabbit has fairly human proportions save the feet), match it or alter the game to use it.
*a favourite video at times like this
