1) Win the Turnover Battle.
With both teams at or near the top of the league in takeaways, keeping the ball is a big priority, and in my opinion, the biggest one. The Bears' offense hasn't been much good - and the Cardinals' offense certainly hasn't been anything to note aside from how bad they've been. And the best way to help an offense is by providing short fields. If the Bears get a couple interceptions to provide a short field.... well, I like their chances to score better than if the Cardinals had a short field because...
2) Force Ryan Lindley to Make Plays
... I don't think Ryan Lindley is really any good. In his three starts this year (six games total) he still hasn't thrown a touchdown to match against his six interceptions. Neither Larry Fitzgerald nor Andre Roberts have topped 700 yards on the season, and Fitzgerald isn't exactly a scrub receiver.
3) Don't Treat Daryl Washington Like Clay Matthews (i.e., Don't Ignore Him)
Sooner or later the Bears have to take down blitzing/heavy 3-4 looks before they can be a serious contender, and the Cardinals have made a living on theirs. Calais Campbell is a player, and Daryl Washington's nine sacks say he's not exactly bad at finding the gap and blasting it for a sack. Really, they'll send anybody. If you lined up on the field for the Cardinals, they'd send you too. The pass protection will need to be aware of where the blitz is coming from on every play... something they had trouble with even so far as identifying a tackle/end stunt.
4) Lean On The Running Game
Teams just haven't been able to pass on the Cardinals this year - for a 5-9 team they really do have quite a good defense against the pass. It probably helps they've only seen the fourth-fewest passing attempts in the league, but still, it's quite good - 22 interceptions, a pretty good yards/attempt, I'll take that. I'm not saying the Bears shouldn't pass at all, but the run game will probably have to be the team's bell-cow in this one. The reason the Bears suddenly went pass-happy against Green Bay was due to the team running something like six offensive plays in between the Packers putting up 21 points. I don't see that happening here.
5) Next Step - Stop Committing Offensive Pass Interference
This could just apply universally as "Stop committing penalties!" but the Bears still employ the same offensive line, so... But anyway, Alshon Jeffery tried to answer our pleas for a consistent second target, but three OPI penalties put the kibosh to that against Green Bay. Jeffery will learn eventually, and against the Cardinals would be a good week to continue that growth.
6) Convert Third Down
So, last week? No third down conversions? Yeah, that's not going to beat any team, including a team with a pass rush as fierce as the Cardinals' can be. Prevent sacks (if only it were so simple!), and keep things in third and managable instead of false-starting 3rd and 1 into 3rd and 6, for example.