The 34-year-old former world champion is on High Kingdom, the horse that took her to team silver at London 2012.
"I have got to have good qualifying. It is also about a good result," said Tindall, the Queen's granddaughter.
"It would be amazing to go to the Olympics, and it is something we are all working towards, but it is competition by competition."
High Kingdom is still to qualify for Rio, having missed almost all of last year through injury.
"The Olympics is the place to be," added Tindall. "It is where you want to be, with the rest of the world's sport. It is a unique championship, and to be able to represent your country there is phenomenal."
Meanwhile, Olympic and European champion Michael Jung will look to land eventing's richest prize by completing the Grand Slam at Badminton.
The German, 33, is hoping to take home the £240,000 awarded to any rider who wins consecutive Burghley, Kentucky and Badminton crowns.
Briton William Fox-Pitt, winner in 2015, is among those to miss Badminton.
Three-time winner Pippa Funnell and New Zealand's former world number one Andrew Nicholson are also absent.
Other British riders looking to secure a place at the Rio Olympics include 2009 winner Oliver Townend and European Championship campaigners Nicola Wilson, Gemma Tattersall and Laura Collett.
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Zara Tindall will look to stake a claim for Olympic selection at the Badminton Horse Trials, which begin on Thursday.