For this achievement, load up The UAC on I'm Too Young to die.
There will be 2 bonus lives and 6 relics in this mission. The relics are shot out of mine/bomb looking things, and the 2 bonus lives look like the doom guy dolls that were collectibles in the base campaign.
Progress can be farmed; they aren't collectibles in the sense that once you get them, they dissapear. Get the 8 items, then reload the level 3/4 times and this will count as progress.
Will take you about 15-20 mins if you choose this mission.
Alternatively, just go through arcade at your own pace and aim for mines and doom guy doll life pickups; this will very much come naturally.