The Tykes, who have been hit hard by injuries this season, have slumped to five defeats from their last seven games and they go into Saturday's Yorkshire derby with Huddersfield just one place above the drop zone.
That form has led to some fans questioning Hill's position, but he remains confident of staying up.
"The demands of the Championship are huge," Hill said. "There are probably 18 teams that really thought they were going to have an opportunity to achieve a promotion place.
"So it was always going to be a tough task but it's achievable.
"We have to be focused on getting the 50 points we need to stay up, it's definitely achievable. We can achieve the impossible dream but it will take a lot of bottle."