ScourgeBringer

As you traverse through the game: you will find computers that can be smashed by pressing your attack button (They look like 90s computers with a green monitor on them). Once they're destroyed they will drop a log item that you can pick up. (After collecting some logs, you can speak to Garo at The Chiming Tree and he will setup a computer so that you can keep track of/reread the logs that you've unlocked too!)

From my understanding whether or not they appear on a level is completely random, as well as what type of log they drop and WHERE on the level they appear (Although I believe rooms with shops, minibosses and bosses are exempt from this rule), therefore it's best to keep an eye out as you grind out the other achievements and collect them as you naturally come across them. There are 2 other log related achievements in total for what I believe is 5 of EACH LOG so don't worry if you've collected a handful and haven't unlocked anything yet (My first log achievement didn't pop until I was roughly 10 logs in).

Update: Thank you to both EliTe I Will and SkarrKilla for confirming that only certain logs appear on a level, i.e Log 1 will only be on realm 1, log 2 on realm 2 and so on. Basically the following:

Logs 1/6/11 Realm 1
Logs 2/7/12 Realm 2
Logs 3/8/13 Realm 3
Logs 4/9/14 Realm 4
Logs 5/10/15 Realm 5

Note that since the maps are randomly generated: the location will vary each time you do a run and you may run into a seed that doesn't even spawn the computer.