Wales only conceded three touchdowns during their entire RBS 6 Nations campaign last season, and they were all scored by Ireland in the opening game as Brian O'Driscoll, Simon Zebo and Cian Healy underpinned a 30-22 Millennium Stadium victory.
Ireland also posted a treble in suffering an agonising late loss to world champions New Zealand less than three months ago, and then repeated it against opening Six Nations opponents Scotland on Sunday.
"We are under no illusions, particularly defensively, of what we are about to face, and we will be hugely motivated for it," Wales assistant coach and defence specialist Edwards said.
"We have got a huge job defensively on our hands this week against one of the top attack coaches (Joe Schmidt) in the world, a team that is in form and scored three tries in 40 minutes against the All Blacks and scored three tries against Scotland at the weekend.
"They have got threats all over the park. You saw from their maul yesterday that they can attack through their forwards, and Cian Healy rampaging over the advantage line, and everyone knows about their backs.
"I think their form at the very moment is very strong. They did a very professional job on Scotland.
"I would say, having come to our ground and beat us last year, that they are slight favourites going into the game, yes. They are playing on their home ground and they are in pretty good form.
"I think they have always been a very skilful, cohesive team. We've always had great battles with them over the years, with the victories ebbing and flowing to each side."
Edwards singled out Ireland scrum-half Conor Murray for particular praise on Monday as the Wales players began preparations ahead of a fixture that promises to have a considerable bearing on where this season's Six Nations title might end up.
Munster number nine Murray shone on last summer's British and Irish Lions tour of Australia, and his battle with opposite number and fellow Test Lion Mike Phillips next weekend should be a key head-to-head.
"The player I am very impressed with is Conor Murray," Edwards added.
"He is a guy who plays with his head up, counts numbers and tries to attack where he thinks the opposition are at their weakest. He has a good understanding with his number 10, so we need to be on our guard."
Wales head coach Warren Gatland is due to name his team on Tuesday, with skipper Sam Warburton and prop Gethin Jenkins both tipped for recalls.
Flanker Warburton began his comeback from a shoulder injury with a 16-minute run off the bench when Wales beat Millennium Stadium visitors Italy 23-15 two days ago, and it appears likely that he will replace fellow openside specialist Justin Tipuric.
The 101 times-capped Jenkins, meanwhile, is fully fit after being troubled by a knee problem, suggesting Paul James could join Tipuric in dropping down to replacement duty.
And Gatland must also decide whether or not he involves centre Jonathan Davies, who played 40 minutes of the Scarlets' LV= Cup clash against London Irish on Saturday - his first competitive action since suffering a torn pectoral muscle three months ago.
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