Most people need between 300 to 400 hours to really feel prepared for the Level 2 exam. If your definition of “go the extra mile” would allow you to get that many hours of prep in before exam day in June, then I say it’s very doable. If you don’t think you’d be able to put that much time, then I would personally say it’s not doable. My two cents!
If you are sure you will pass and can hit the books right away for level 2 following the level 1 exam, it should be do-able. If you are going to wait on results for L1, then it will be more challenging, but still do-able.
Also, it depends on your background. If you are solid in FRA, Corp Finance and Equities, L2 should be a breeze. I personally found L2 to be easier than L3, but it has more to do with my background knowledge and experience, so it is different for everyone.