She is Engaged to a Guy, How Do I Attract/ Impress/ Woo Her?

She is Engaged to a Guy, How Do I Attract/ Impress/ Woo Her?

You've mentioned that she is engaged, and she is very reserved, because of the cultural upbringing.
Things you have to notice:
1) She is engaged to a guy who is 8 years older to her.

2) She is not the type who would very likely break off the engagement, even if she wants to.

3) The guy is old. He won't let go of the girl that easily either. He is probably taking care of her very nicely. And she feels safe and secured around him. (This is only conjecturing)

The point is, you're a threat to her future matrimonial prospects. Stop being that. If she did like you, then obviously she lacks the courage to face the truth and call off the whole marriage. It's time to face the truth, my friend. Some people lack the courage to do what they really want to, the reasons for it could be plenty: to avoid a social mess, to avoid a scene, cowardice, confusion, lack of confidence, and also, being stupid.
I presume your're from India, where women from reserved families are very much conscious about society, family, and what people think about themselves. You mentioned she is engaged to a Guy 8 years older to her but nowhere mentioned they are in love, so I am assuming it's an arrange marriage. (Because she liked you)
The chances of breaking her engagement, getting her with you, are very very less, not because there isn't a way, but because of this particular girl.

Anyway, How to break up an engaged girl?

1) Find out what the guy is like, because you will have to outdo him in some way.

2) Hang out with her as much as you possibly can, but don't overdo that. She should enjoy your company as well, and be equally willing to hang out with you too.

3) No guy in this world, likes another straight guy hanging out with her girlfriend/ fiance. At one point, he will start getting jealous from you, and have problems. If you're close, she will defend you which might lead to some fights. If he is a gentleman about it, then you're doomed.

4) Suddenly talk a lot about what she wants to do in her life. This is a long shot, but many a time, women sacrifice their career to marry a guy. You can always ignite the passion for her career again. This is a major engagement-canceler.

5) Tell her bad stories about failed marriages, BUT NEVER CONSCIOUSLY ADVICE HER THAT YOU'RE AGAINST THE MARRIAGE. Make it look like you just heard a story. Play cool.

6) Every guy has a weak spot. We are guys. If you'd try, he will have a weakness, such as alcohol  gambling, (you know where I am going.) Once you find out about it, DISCUSS (Only discuss, do not pass any judgements) with her, make her talk about it as much as you can. It leads to two possibilities:
 - She would either be over it, by talking about it openly.
- You will find some problems that she is hiding beneath denial.

In both the cases, she is talking about irregularities of her boyfriend/ fiance, it will stick in her head. She will remember them which will come out in some aggressive manner.

7) The thing is, most women are really fond of the idea of marriage and have always pictured their lives going this road. So it is very hard to get a girl out of a marriage, whereas with a guy, it's a matter of an hour.
If she has no career ahead of her, and looks for nothing but a married life and has already found a guy, then the only thing you have is to be the guy.
You'd have to make her fall in love with you.