I do think there should be a "report tweet" button associated with the specific tweet.
I would imagine she became a target because of her high profile following organising a campaign to get womens faces on UK banknotes- Jane Austen on the £10.
There is a trend right across different interest groups on the internet right now to target women who develop a high profile. These women then get death threats vile language and threats of rape. It must be borne largely out of low self-esteem by some males, who, when they view the world, see only preferential treatment for women and loss of power status and respect for men. There are even organisations for this - MRA - Mens Rights Association or similar- where you will find odious and mysogynistic articles and comment.
At least some of it is idiot teenagers jumping on some bandwagon that they think is cool without fully appreciating how disturbing such threats could be, but even discounting them, you will have a whole bunch from sad males who think women are getting uppity.
I am not entirely sure how twitter works. I don't know, for instance, if all tweets are saved for posterity - I understand that there are 400,000,000 tweets a day, so that takes some archiving. And I know that when I log in to my twitter account, I only scan back for the last few hours worth of tweets, so it can be epheremeral - but imagine how disturbing it would be to get 10s, 100s of threats and vile language every hour simply for campaiging for an equality issue?