She sees herself primarily as a barrister - she became a senior counsel in Hong Kong in 1997 and is a former chair of the Bar Association - but almost all her time is taken up with Legislative Council duties and her policy focuses of high-quality education, environmental and nature conservation, and medical and health issues.
Her move into politics was largely accidental. Ten years ago, the Democratic Party asked her to run as its candidate in a by-election. "My first reaction was, 'you're crazy!' - it was so far removed from my gentlemanly life as a barrister," she says.
While put off by the prospect of having to promote herself to seek election, Eu found she could also promote the causes she believed in. She became a political convert and a highly regarded spokeswoman for democracy, equality and social justice.
In 2006, she founded the Civic Party, which she still leads. On a typical day, Eu attends several Legco meetings from 8.30am until 6.30pm. Before and after that, she meets people, lobbyists and the media, and gives speeches. She believes in the importance of bringing politics into people's lives.
Now that her children are grown up, Eu devotes most of her time to her work. She is married to Edmund Woo, and the couple have three daughters aged 26, 23 and 17. The girls show signs of inheriting Eu's predilection for pushing themselves to achieve the best of their abilities.
The eldest daughter is studying for a PhD in chemical engineering at the University of California, Berkeley, where her papers are published in leading industry journals. Her second daughter is studying accounting, while the youngest is at secondary school abroad.
Eu says she is driven mainly by a sense of duty. "All my life, I've worked on the [premise] that if I don't take on the challenge, I'll never know if I could do it. I push myself to do it, every time," she says.
In June, her acceptance of Chief Executive Donald Tsang Yam-kuen's challenge to an unprecedented live television debate on the government's 2012 political reform led to a performance in which she was widely deemed to have outshone her challenger. At home, Eu says her husband is a tower of strength.
"I have very good family support. My husband looks after me. He supports me in whatever I do."
Holidays allow the family to spend time together. After several failed attempts at skiing, Eu made a breakthrough on a recent holiday. Her instructor advised her to trust in the law of gravity and to lean forward - "almost as if you're embracing the mountain".
"The moment he said it, I understood," she says. "Skiing is just like life. You have to stretch your arms forward and really throw yourself into it, and that's the way you keep your balance."