There are 160 collectibles in the main game during a single Playthrough, so you can miss a few and still get your achievement. This guide is for both this achievement and the, "Nearly There" achievement which requires 120 collectibles.
For starters, both of these achievements are cumulative. Meaning that once you get a collectible, that will be forever added to your 60 and 120 required for the achievements. This means, you can play as different characters and pick up the same collectibles in a different Playthrough. This also means, you can quit out of the game at any time, and your progress will be saves.Collectibles include:
I can't really give you many tips on where to find them, but I will tell you as much as I can. You just want to keep an eye out for them. They're normally inside buildings, safe areas, on benches & rewards for completing quests. You can go to the arena and pick up the Collectible on the table in front of you. There is also a collectible in each Arena.
If you want to farm Collectibles (Which I really don't recommend), you can keep making new characters and picking up the same collectible in different Playthroughs.
Video Credit: TheEmberstrife
Here is a list of a full video collectible walkthrough. Although I didn't use this, it may be useful to someone. Just click on the video title at the top and it should take you to a full Playlist.
Also, I got my 120 a little after reaching the Laboratory in Act III, which is where I got it the 2 times I earned this achievement before.