I also applied at BSA (Germany) and had collected some information online and from friends and other connections/forums.
First, there's a normal phone interview. If you pass that, you will get invited for the case interview at BSA. There will be 2 rounds in the typical case interview format (personal fit, case interview...). This is for the entry level. For the level of senior associate, you will additionally have to do a presentation.
BSA was #1 hidden champion 2015 (http://www.berylls.com/en/hidden-champion/awards.php), they won the Best of Consulting 2016 award in a category (http://award.wiwo.de/boc/rueckblick/). I recommend you to go thru their press releases on their website, it contains loads of information.
The starting salary is according to industry standard.
You have to be passionate about the automative industry, and preferably you should have internships or other work experience in the automotive industry on your record. From what I have heard, you need at least a 2.0 GPA (in Germany) and a good grade in Maths. Also, some people mentioned that Berylls doesn't prefer candidates with a degree from a university of applied sciences (FH)) and candidates coming from Big4, but I don't know if this is always the case.
If you find any more info, feel free to share it with me, as well ;)