Ledesma, who is set to win his 82nd cap, has already announced his retirement following the tournament in New Zealand and will coach the forwards at Stade Francais.
The Pumas lost 13-9 to England in their opening pool match, meaning they must win tomorrow and next week's match with Georgia to have any hope of progressing to the quarter-finals.
Ledesma said: "For this group of players this is the biggest match they have had. It doesn't matter what they have played before, it's this game that matters.
"For me it might be the biggest battle in my career. It's one of those phrases you always use - the next game is always the biggest.
"This might be the biggest, but it might also be the last. Hopefully there will be four more (to the final).
"We have prepared very well. We did everything we could to be in the best shape and have prepared for this game in the best possible way.
"We're spiritually very calm, we know we've prepared well and it all comes down to what happens on the field.
"I'm just happy we've done everything in our power."
The 38-year-old, who made his Test debut in 1996, knows what to expect from Scotland.
Ledesma believes the selection of Ruaridh Jackson at fly-half means Scotland have shown their hand early.
He added: "Scotland are looking to play a game with many phases. They will be trying to force us into penalties.
"They have got the belief that after the fourth phase we'll give away penalties, so it's our goal not to."
Ledesma will also hope to help the Pumas gain supremacy at the set-piece.
He said: "The Scottish scrum is the weak point but they have worked a lot on their scrum and now they're stronger.
"A good scrum in the World Cup is important; Australia lost the scrum to Ireland and that was it."
Ledesma's front-row colleague, loosehead prop Rodrigo Roncero, agreed with his team-mate.
Former Gloucester prop Roncero said: "When the whistle goes tomorrow it doesn't make any difference what happened before and the whole four-year cycle will depend on tomorrow's game.
"Tomorrow's game is crucial, the game that really counts."
Scotland are tomorrow without tighthead prop Euan Murray, a player regarded by their head coach Andy Robinson as his team's leading scrummager but who refuses to play on Sundays due to his religious beliefs.
Roncero, though, does not believe Murray's loss impacts too greatly on Scotland.
The 34-year-old, who is now at Stade Francais, said: "Scotland use Murray a lot at scrum time. He's very important.
"It's a different type of scrum with and without him.
"It doesn't necessarily mean it's weaker, but it just means when he's on the field it's a different kind of scrum."
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