Easy "World's Snazziest Dresser" achievement or troph
The two easiest costumes to unlock are "Year One" (by linking to WB Games) and "Beware the Batman" (by playing Batman Arkham Origins). Only four other suits are required to earn "World's Snazziest Dresser": "Blackest Night" (by finding the five pieces) and "New 52", "Red Son" and "One Million" (by finding four pieces, then defeating a particular Boss last). Thus, three playthroughs will be required in order to unlock each of the three final suits.
Easy "Fresh Beats" achievement or trophy
Cape-stun a large enemy, then beat him to death with bull-punches. This must be done ten times.
Easy "The Collector" achievement or tropy
Besides finding all detective cases and obtaining all the pickups and upgrades, you must also unlock all the batsuits.
Easy "Breathless" achievement or trophy
The first chance to earn this happens after you enter the administration building. The Joker will pump poison into the room. Remain there for a few minutes until you die.
Easy "Bad Case of the Mondays" achievement or trophy
When Grundy's health is low, force him to walk over water. Throw the Shock Batarang into the water to achieve the killing blow.