...Manufacturing process... is a tighter and therefore better phrase than ...process used to manufacture..., so your fellow-translator was right on that score. Since that's just a stylistic judgment call and you're the judge here, though, I assume saying so precludes my winning the bounty. ^_^
Analysis of the stability of the manufacturing process of Atinumab, substance-solution
It's the rest of the title that's the real problem, though. You want something punchier if at all possible.
First, unless there is some other document analysis is being contrasted with (e.g., research or findings), it's actually unnecessary. If this is a document concerning the stability of the manufacturing process, its role as an analysis of that topic goes without saying.
Stability of the manufacturing process of Atinumab, substance-solution
There's just no way that the product name, as given, is actually grammatically correct. Either substance-solution really is an appositive phrase or it is a fundamental part of the name. If the former, it shouldn't be included at all unless there is another form of Atinumab with which it's being contrasted. If it is being contrasted with another form of Atinumab, it'd still be better to use the term as an attributive adjective than an appositive phrase. If it's the latter, it shouldn't be shunted off by a comma and left lower-case. English names don't work like Russian ones: It's the Black Sea, not Black sea, and the Volga River, not Volga river.
Based on what you said above, I think this is the correct formatting
Stability of the manufacturing process of Atinumab Substance–Solution
though obviously you can't change the product's name if marketing already gave it to you in a different format.
Note also the en dash instead of the hyphen, since you're using it to replace an implicit and between those two nouns. Again, this may be mistaken or something that marketing has tied your hands regarding, but cursory googling shows that hyphenated or dashed substance–solution isn't accurate. Instead, everyone seems to write it as two words, substance solution, with the first acting as an attributive modifier towards the second. So more likely
Stability of the manufacturing process of Atinumab Substance Solution
if you have an audience who is more comfortable with British English or
Stability of the Manufacturing Process of Atinumab Substance Solution
if they're more used to the American style of title capitalization.
Either of those seems to be grammatically correct for whichever side of the Atlantic you're writing for. It's still an awkward title, since it's overlong. Either of
UK: Stability of the Atinumab Substance Solution manufacturing process
US: Stability of the Atinumab Substance Solution Manufacturing Process
is going to be about as tight as you can make the phrasing while still emphasizing that you're looking at the stability of the step-by-step process of manufacture. If you're just discussing the manufacture in general or as whole, you could go a step farther to
UK: Atinumab Substance Solution manufacturing stability
US: Atinumab Substance Solution Manufacturing Stability
If the comma really is necessary for the product's name, there should be one both before substance and after solution.