The Hoops have yet to register three points in their two Scottish Premier League encounters with Pat Fenlon's men, with the first game at Celtic Park ending in a 2-2 draw and Leigh Griffiths' breakaway goal proving decisive in the capital.
Wales international Ledley has yet to feature against the Easter Road side during the current campaign, but knows Celtic could retain their SPL title if they beat Hibs and second-placed Motherwell lose to St Mirren.
"Hibs have done really well and have some good individual players," the Welshman told this week's Celtic View.
"Leigh Griffiths has done well for them. They are organised, but hopefully we can break them down and beat them for the first time this season. We know it will be difficult because of the way they play but with our home form, we can achieve it.
"They have got dangerous players going forward so we will need to try and keep at things on the back and try and keep a clean sheet.
"We always feel we will always score goals at home and that's what we will need to do in the next game but keep the back door shut."
Ledley has been impressed by Hibs' progress under Fenlon this season but insisted that the Celtic players were eager to end their poor record against them in recent fixtures.
"They have been a tricky team this season and have shocked a lot of people, considering they didn't do as well in the last campaign," he added.
"Their manager has done a great job for them but now we need to get a bit of revenge and try and get a victory."