Is there any way to escape a terrible cumulative grade average? I am an undergrad student studying engineering at one of the top institutions in my country. Doing this degree was not my original plan and I came to it after I was unable to gain full financial funding to study at a prestigious music college overseas in the United States which I got into on a partial scholarship. Regrettably I entered this degree with the mentality that because this was not what I had originally wanted to do it didn't matter if I achieved highly or whether I just passed. I was there to get the certificate. I have what I consider to be a very poor academic record due to bad study habits which have led to me having to do several rewrites of exams despite walking in with decent predicates. At my university when a student does a rewrite the final mark is capped at 50% (We work in percentages and not GPA like in America) and so my academic record is littered with these 50% results for modules. 

I am nearing the end of my undergraduate career and sadly only now after having failed a module for the first time last year have realised that a little bit of hard work before exams can actually produce really great results, and that I am capable of doing so when I set my mind to it. In the past year I've become more interested in my field of study and in my own free time have made considerable progress learning a particular foreign language. I recently found a postgraduate scholarship to study overseas in the country where this language is spoken. I think I would stand a good chance of getting it however the minimum requirement for application is 65% in previous studies. Masters programmes in my own country also require this 65% average in past studies. My average currently sits at 59% (equivalent an E in the US) and I have worked out based on my remaining modules that for all practical purposes it will be impossible for me to raise my cumulative average to 65%. In fact even if I get distinctions for all remaining modules I can at most raise my average to 61% (equivalent C in the US). 

I know my abilities and that I have many fantastic qualities that would be desirable in a postgraduate environment however I feel that I've now somewhat shot myself in the foot for future studies due to very poor choices in my past. I feel like if anyone looks at my academic record they will only see my potential based on that cumulative average. Is there any way to escape a terrible cumulative average and to continue down a more academic path?
Perhaps something to look into are post-baccalaureate programs. I'm not sure about in your country, but in the US there are a handful of post-baccalaureate programs for students in your situation -- students who want to go to graduate school, but haven't performed well enough academically in undergrad to have a good application. The programs vary, but usually consist of a year or two of courses on a particular subject and a certificate is awarded at the end.

A friend of mine wanted to go to medical school, but she went to a very difficult engineering school for her undergrad, and thus had a low GPA and didn't get into any medical schools the first time she applied. So she did a one-year post-baccalaureate medical program, where she excelled academically, and then applied to medical schools again and got accepted.