Upon starting the game, when you see the body on a slab, hold down the X button to start the incinerator and burn it. Watch the following cutscene and when you gain control, you'll be using a cop named Officer Owens that's inside of a diner. After someone comes up to you and complains about someone smoking, head to the corner booth and things get real very quickly. Feel free to shoot anything if you want, but it doesn't really matter, so just wait it out until the scene ends.
When you regain control, you'll be Batman, so jump off of the building and hold the X button to glide. Combine this with R1, when you can, to use the grapnel boost to get across Gotham and to the designated marker, where you'll meet up with Gordon. After a conversation with him, and then Oracle, head to the next location to find some thugs harassing an officer. Drop down and take care of them, being careful of the one that charges, then help the officer.
You should get a prompt soon to "even the odds," which basically means summoning the Batmobile. Once inside, get used to the controls a bit and chase after the vehicle that almost hit you before on the ground. Luckily, there are arrows on the ground that will guide you to your destination, so make use of them to follow the car. Watch out for the RPG blasts, which are marked as they fire and retaliate with your own shots when you see the marker lock on.
Hit the vehicle with two of these and then either one more or hitting it will put it out of commission. Approach the vehicle (if there's any enemies nearby, you'll have to take them down before you can go after the driver) and interrogate the driver when close enough. Well well, it looks like we got a sample of Scarecrow's new toxin, as well as a lead on his location.
Get back in the Batmobile and head to this location, where you'll need to get to the top of the building. Now, if you want some extra XP, feel free to smash the guards outside of the building, but if you just want to continue, get on the roof and smash down though the glass. Note that one of the enemies inside has a gun (the other gun is inside a room and won't fight you), so if you can get a Takedown on him through the glass, you won't have to worry about being shot.
Defeat everyone else and after a few scenes, you'll be outside with Poison Ivy. Before you can do anything, some tanks show up, which will prompt Batman to bring out the Batmobile. Hold down on the directional pad and select the remote control for it, which will make it show up and take out all of the enemies on its own. The Batmobile in this game has a Battle Mode, which you can toggle off/on by holding down L2.
While in this mode, press R1 to fire riot-suppressing shots and R2 for the 60mm Cannon. You'll be using the latter to take out a wave of tanks that will be coming to your location shortly. You can easily avoid their fire, which has its trajectory shown, by pressing X while holding in any direction. Once all of the tanks are destroyed, head back to Batman and Ivy and drive into the designated marker on the ground.
Batman will load up Ivy and before you take off, you'll have to make a quick stop first. Head to the marker and start the challenge, which will unlock a new attack for the Batmobile. Basically, as you destroy enemies in the vehicle, a meter will build up and you will be able to fire missiles, with there being one at level 1 and four at level 2. After finishing up the training, you'll need to head to the new marker, where you'll face off against a lot of drones. Use the missiles, along with dodging to destroy them all.
With that all done, escort Ivy to the police station and go inside, where you're free to explore. The objective, although not shown, is to go to where Gordon is, which will initiate a short scene that will set your next mission, as well as open up some of the Most Wanted side missions. Before you do that, however, go into the Evidence Room to find a Riddler trophy, as well as a new gadget for Batman (both will be behind fragile glass that you see in Detective Mode). Break them both to get the trophy and the Remote Electrical Charge.
Now, go to Gordon to get caught up on the latest news. You can either continue with the story or start one of the other Most Wanted side missions, which can be accessed by pressing right on the directional pad.
