Akshara was always like this.
The writers tried to develop this "aarohi akshara" soul sisters angle since they were kids. Like others mentioned, Akshu, as an infant, would save her sister in impossible situations and at that time Aaru did reciprocate. Sirat and Kartik were shocked ("asa connection toh twins main hota hai?") cause they were in sync w each other and their mom. But with time, Aarohi grew into this very insecure person but I don't think that's entirely Sirat's fault cause the thing she was insecure about most was Sirat and her relationship. She felt Akshara was favoured by Sirat so it couldn't have been Sirat that inflated Aarohi's ego of "being number one". Rather, the entire family was dismissive of Aarohi's ill temperament. From what I remember, rather than correcting Aarohi and teaching her, Manish just rebuked Sirat, her "bad blood", and told her to handle it. I haven't grown up in a joint family but I found that unusual that the elders aren't involved in the parenting much. Even now, as orphans Manish and gang are very uninvolved with their lives. They hear the good news from the girls but very much oblivious to what's going on in their lives.
But none of this explains how she went haywire enough to lie about everything and try to commit fraud for a seat in that exam.
Anupamaa
15