Okay I'll have a stab at this. Pretty much what I've down on other boards.
We need to open with the turtles
Almost every version of TMNT from comics, to the various cartoons and movies has has started in a similar way. We get a bit of suspense were the audience knows the turtles are there but we don't fully see them for a while before we see them going into action.
The turtles need to be delivered in a timely manner even if we don't see them again for a while. I know that was the point of the quasi-animated intro as well as supposed nod to the comic but it was a weak opening that felt tacked on with overly cheesy narration.
May I suggest taking the opening from the original comics TMNT #1 which has been recreated to varying degrees by almost every version.
Casey Jones
I'd personally prefer it not be the Eastman suggestion that he became a vigilante from watching too much bad TV although I quite like the first movie's deleted scene take on this and Casey sick of seeing so much violence around him decides to take up a cause. That might be cool to actually see on screen.
But he needs a back story and my suggestion is working in the one from the Mirage Tales of the TMNT #56 and 2003 animated series episode Meet Casey Jones were Casey's father owned a store but refused to give in to a street gang (The Purple Dragons) so they burned down his store with a hint that Casey's father was in it when it was torched.
Hun & The Purple Dragons
While it doesn't necessarily have to have the leader of the gang be called Hun or for the gang itself to be called Purple Dragons I think we need to see some street level organised crime. Like a real life gangs have 'The Dragons' have the modern Foot symbol tattooed on them just like in the comics too. You've used the modern Foot logo in the movie already so it's already established.
Have them connected to the Foot Clan via their leader who would essentially fills the right hand man to Oroku Saki in the movie. This could be the very same gang that Bebop and Rocksteady are a part of and Hun volunteers them for Saki's experiment with the mutagen after their defeat at the hands of the turtles near the beginning of the movie.
Foot Clan
Yep. Foot Clan as in an actual international organised crime group with their operatives as trained ninjas that act in the shadows. Not just like in the comics but in real life gangs like the Yakuza.
Ditch the whole NY based para military terrorist group. I don't know why anyone would think this was more realistic than organised crime group using martial - we have them in real life. They can still use guns but not as much.
TMNT & Splinter Origin
My better judgement tells me that it's best left alone and forgotten but as fan I will have this niggling feeling watching the movie that it's not right so a do-over that fixes the origin is necessary.
I'd personally avoid the reincarnation angle from the IDW series. Rather stick to the classic comic origin simply say that the mutagen awakened memories of watching Yoshi train as well as watching Yoshi be murdered by Saki.
Turtles with Real Personalities
The turtles personalities were technically "correct" in their broadest term but they were never given much time not act like complete caricatures. We need some downtime with them to show there's more to them than being one-note characters in the same way that every other version has done.
Bebop & Rocksteady
If they are going to be in this then they have to be somewhat menacing and when they are mutated animalistic. Not the brightest sparks but competent enough to put up a good fight with their strength akin to the first season of the 1987 animated series.
Themes
Vengeance.
- Oroku Saki wants revenge on Yoshi for Tang Shen not loving him.
- Splinter wants revenge on Shredder for killing Yoshi.
- Shredder wants revenge on the turtles for stopping his scheme in the first movie (as well as eliminating the last remnants of Yoshi)
- Casey Jones wants revenge on Hun for killing his father
- Bebop and Rocksteady want revenge on the turtles
However a small suggestion from personal favorite version of the Bebop and Rocksteady from Archie's TMNT Adventures series that at the end they decide that they don't care for all the battling and leave for a peaceful life. They only two who learn are the stupid ones.
What I Don't Want to See
Vern Fenwick, Taylor, Eric Sacks, over abundance of accessories on the turtles, permanent sun glasses on Raphael and Michelangelo.