Playing as Aldrich Killian: die and respawn
Aldrich Killian is unlocked in the level ‘Ready A.I.M. Fire’ via a character token. You can collect it in either Story Mode or Free Play. In Story Mode, he is in the first section of the level (Tony Stark’s Malibu house). In Free Play, he is located in the ‘Part A’ checkpoint. Once you’ve unlocked him, you can purchase him for 85,000 studs.
This is easily unlocked if you replay a level in Free Play. To replay a level, while in a hub, press and select ‘Go to Space’. Then select any level and choose to play it in Free Play. Select Aldrich Killian as your character. When it starts, just allow him to be defeated, and when you respawn the achievement will unlock.
Thanks to VGFAQ for the Aldrich Killian character token location (at 6m 40s):