Kill all of the henchmen that are celebrating at your party when you arrive and you get the Party Pooper trophy.
To get the Night Glider achievement, you need to make Batman glide for over 100 meters without jumping, using a rope, or anything else.
To get the Rope-a-dope-a-dope trophy, you need to grab up a henchman and then drop him on a second henchman to surprise him.
Mano-A-Mano trophy means that you beat the Titan henchman and don't use a single Batarang.
To get the Catch! Trophy, you catch a Batarang - which is pretty easy to do.
To get the Freakshow Rodeo achievement, you simply have to ride the Titan henchman until you have pushed down 10 mobs. This is a fun achievement to get!
If you can get the Spirit of Amadeus Arkham to reveal itself, then you will get the World's Greatest Detective achievement - which is NOT an easy task.
Beat 100% of the whole game, every area, and you will get the Perfect Knight achievement.
Get every other trophy in the whole game and you'll get the Platinum trophy.
Beat Zsasz and get the Shocking Rescue achievement.
While you're at it, save Dr. Young from Victor Zsasz and you will get the Zsasz Cut Down To Size achievement.
If you manage to save all of the guards and the henchmen from the toxin that the Joker puts out, you'll get the Leave No Man Behind achievement.
Somehow you manage to not die during the massive waves of deformed henchmen that the Joker sends your way and you'll get the Malpractice Needs More Practice trophy.
Get out of the Intensive Treatment up to the surface of the island and you'll get the Born Free achievement.
Want Just What The Doctors Ordered you need to save all of the doctors in the medical area of Batman Arkham Asylum.
Are you a Daydreamer? If you managed to survive the onslaught of the fear gas from the Scarecrow then you will be.
When you Resist The Fear by beating all of the effects of the fear gas then you'll gain this achievement.
Miss Bane from the older Batman movies? Well, if you can defeat him this time you get the Baneful Payback achievement.
When the Joker takes and locks you out of Wayne Manor, get back in and you will get the Breaking and Entering achievement.
When you finally face your fears in Batman Arkham Asylum, you'll get the Recurring Nightmare trophy.
Poor Harley, if you can capture her and lock her up, you'll get the Solitary Confinement trophy.
Beat two henchmen at one time and you'll easily get the Double Trouble achievement.
Killer crock? In Batman Arkham Asylum, if you can go into the croc's lair and live to tell the tale, then you'll get the Crocodile Tears trophy.
Take down the giant poison ivy plant and you'll get the Poisoned Ivy achievement.