Creative synopsis

INDIRA GANDHI

Mythos: you can’t tell the whole life story of your protagonist. So, where would you choose to begin and end the action?

beginning: being elected as leader (1966) That's a good point of departure, as it puts her in a position of 'good fortune' at the outset. One possible drawback: how could the 18 years between this point and her assassination be covered on stage? Extreme selectivity would have to be exercised.
ending: did not mitigate the tensions and struggle for independence of the states, killed by her bodyguards A very clear end point! But it's worth thinking about what might happen on stage after her death. Look at how other characters in Antigone and Phaedra, for example, react to protagonists' deaths.

Ethos: what kind of a person is your protagonist? (This means their fundamental, permanent character traits – not temporary phases that they go through)

determined
strong leader
stubborn? strong-headed? A good choice of character traits. As the example of Creon shows, the dividing line between determination and stubbornness can be a powerful element in a tragic protagonist's character and reasoning

Dianoia: how does your protagonist respond to situations, challenges, etc.?

strives for power and influence at all costs
does not negotiate with the rebellion, but orders the Indian army to attack them. As you note below, this can be seen as her hamartia

Peripeteia: is there a surprising reversal in your protagonist’s situation? A reversal of this kind can’t come out of thin air – it has to be logically connected with the rest of the plot. How could this connection be made?

first time in the history of India for the INC to lose the election
unexpected reversal of support Good point - and it would be possible to make sure that this is a genuine case of peripeteia, as opposed to an ordinary reversal of fortune, by showing how it ran counter to expectations. For example, you could show that IG's assumptions of electoral success were based on supportive press coverage, which had helped her in the past but didn't show the strength of anti-Congress feeling in the country. Having said all this, the electoral defeat of 1977 isn't directly related to her eventual assassination - so it may be difficult to integrate it into a tightly interwoven plot.
1980s- Punjab and Sikh states struggle for independence, and she presses against that
Is eventually killed by her own Sikh bodyguards This seems to offer the most potential for peripeteia. Again, you'd need to make sure that expectations are radically overturned. To do so, you might need to develop the bodyguards - or someone who controls them - as significant figures in the action, show how careful IG was to ensure the loyalty of her bodyguards, etc.

Anagnorisis (‘recognition’): does your protagonist gain knowledge in a way that affects their downfall, e.g. realizing that they've done something that they wouldn’t have done if they'd been in full possession of the facts?

no? she dies before she can acknowledge So if you wanted to introduce an element of anagnorisis, how could you do so? Maybe invent a moment of recognition shortly before her death, during which she reflects on her error in ordering Operation Blue Star?

Hamartia (‘error’): what crucial error(s) does your protagonist make, and how do these cause their fortune to change?

leads from change from good fortune to bad fortune
when the states start using violence to assert their demands for independence, rather than negotiating, she responds with violence(Operation Blue Star 1984)
she is killed in her garden by her own Sikh bodyguards.