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You should use Detective Mode to identify destructible walls or floors and grates that can be removed. For grates that appear out of reach you need to use the Bat Claw which you’ll pick up on your first visit to the Bat Cave. For walls and floors that can be destroyed you’ll use the Explosive Gel which you get from the Bat Mobile. Simply spray it on and then detonate. You also need to look out for places you can zoom up to using the Grappling Hook, there are loads of them.
Detective Mode also gives you information on people in the area and sometimes on machinery. For example when areas are flooded with poison gas the solution is to use your Batarang to hit a control box and turn on the fans. You’ll also sometimes follow clue trails using Detective Mode.