I haven't done this myself, but I did study a lot of ancient Greek and got a PhD in philosophy. In general, I don't think it is insanely difficult to do this if you are a good student. But I would think hard about your long-term goals. Basically this degree is only useful for being a classics professor. Are you sure that's what you want to do? Also, if you are, you should probably go to one of the top 10 or so graduate schools for classics. If you only get into second-tier schools, you might have a hard time getting a job or only get a bad job. Finally, I would add that even in grad school lots of students are imo not very good at Greek and Latin. I would approach learning these languages in as similar a way as you can as how you would approach learning a normal, living language. If you can get fluency with them, you will have a big advantage.