Story Progression Achievements
You get an achievement for each level you complete, so just playing the game is the easiest way to get them. For example, you get the "Hero" achievement by completing the first level with a hero character. The "Kill-a-Moth" achievement is awarded just for defeating Killer Moth. Some achievements are awarded for building items with LEGO blocks. The "Make It Snappy" achievement comes after you build Killer Croc's ride-on in the second villain episode.
Hero Achievements
Most of the superheroes in "LEGO Batman" have their own easy achievements. Do 20 back flips in a row as Robin and you get the "Boy Wonder" achievement. Use Batman's Batarangs to destroy 10 objects in one throw to complete the "There and Back" achievement. As any hero, smash every street light in the first level to unlock the "Natural Habitat" achievement. To get the "Justice League" achievement, buy Batgirl, Nightwing, Commissioner Gordon and Bruce Wayne in the LEGO store using the money you collect during levels.
Villain Achievements
The members of "LEGO Batman's rogue's gallery also have a set of achievements. Freeze 50 enemies as Mr. Freeze to earn the "Ice to See You" achievement. Use Scarecrow's scare toxin five times to unlock the "Scare Tactics" achievement. To unlock the "Throwing Up" achievement you need to throw 50 police officers using a villain with super strength like Bane, Killer Croc, Clayface or Man-Bat. These are easy because they only require the villain's standard attack and the feat can be accomplished in one level.
Multiplayer Achievements
You can get the "Sidekick" achievement just for completing a level with another player. Have one player select Commissioner Gordon and the other Harley Quinn, then use Harley's hammer attack on Gordon to unlock the "Smash Gordon" achievement. Select Joker for both players and have one Joker use the shock attack on the other to unlock "Start of Something Wonderful." With Bane and Batman as the playable characters, use Bane's backbreaker attack on Batman to unlock "Atomic Backbreaker."