With regards to your 13th mth salary, the company should give it to you pro-rata, even if you leave before a full year. That's because the 13th mth salary comes about from the fact that there are 52 weeks in a year, but only 48 weeks in 12 months. So, each full year, you actually work 13 mths comprising 4 wks each (as opposed to calendar months).

On the other hand, if your employment contract (I assume you're paid more than the threshold of the Employment Act) doesn't stipulate that a 13th mth salary is payable under contract, then you or may not get it, depending on company policy towards resignees.

So, ask your HR first if they will pro-rata.

With regards to your boss, she's trying to tell you that you're not what the company is looking for and you should quit, rather than force her to sack you. My advice... don't fight it. Your boss obviously doesn't want you around anymore and will be against you from now on. Why make yourself suffer under a boss who wants to get rid of you?