Healy's side won their opening two matches thanks to stunning rescue knocks from Ash Gardner, against New Zealand, and Beth Mooney, versus Pakistan, aided both times by some dogged assistance from the lower-order.
But with India also having faced their own batting trials and tribulations, coming off a shock defeat against South Africa at the same Visakhapatnam venue on Thursday, Healy expects both the two favourites' big guns to start delivering at Sunday's sell-out.
Asked if she was concerned at seeing her side endure two laboured World Cup wins off the back of a tight 2-1 victory in the ODI series against India, Healy shrugged: "No, not really.
"I mean, we're allowed to lose games of cricket and we're allowed to be put under pressure at times, in particular in World Cups.
"You're going to be put under the pump in unfamiliar conditions, against unfamiliar sides at times.
"I really back our depth in our side and our squad, that the 11 we put out on the park are going to be able to get the job done for us.
"And we're fortunate it's been a different person every time that stuck their hand up and said, 'yep, I've got this, I can get us to a total' or 'I can take the wickets to restrict the team'. So I wouldn't say it's a worry.
"It's something we'd like to rectify ... on the kind-of-collapse situation in the last couple of games, I think it's on our top-order to make the bulk of the runs - and I think we can speak on that from both sides."
The hosts will doubtless agree with their star batters Smriti Mandhana, captain Harmanpreet Kaur and Jemimah Rodrigues having all misfired so far during the tournament.
On Thursday, they all fell cheaply, leaving it down to Richa Ghosh to pull out a big-hitting 94 at No.8, which was still not enough for them to avoid defeat thanks to an even more astonishing knock from the South Africans' own 'great eight' Nadine de Klerk (84no).
Asked whether she still considered Harmanpreet's side to be the champions' main rivals, Healy said: "The rivalry continues to grow. I feel like India have been almost a sleeping giant in the women's game for a long period.
"It's probably since the Women's Premier League that they've realised the depth they've got and they've figured out a style of play they want to want to use, especially in this format, which has been really impressive to see.Â
"In their home conditions, they're obviously going to play really well and be a real threat, but as we've seen throughout this World Cup so far, there's lots of teams that are pushing everybody.
"So I wouldn't probably say there's one team that's our main threat. We know we're going to have to work hard in every fixture to get our result and that's the way a World Cup should be."
