The collectibles are the artwork and music tracks you can unlock for completing challenges and acts.
Sufficed to say, rather then listing the items individually with their prerequisites, I'll simply tell you what you need to do to get this achievement.
Completely EVERY challenge for both Modern AND Classic sonic (Rank doesn't matter, as long as you clear the challenge).
Complete EVERY Act for Modern and Classic sonic (This obviously unlocks the challenges).
Get EVERY Red Ring for each Act.
Now, once you've cleared the challenge, you'll notice above the gate that a bell has appeared. Jump and hit that bell, you'll see a music note fly out and bounce around the map. You have 20 seconds to catch that note. Blue notes are for artwork, Gold are for music tracks. You'll need to collec these from ALL 90 challenge gates (Classic and Modern) for the achievement to unlock.
You can tell if you've collected a track or artwork already as the bell will go from shiny gold to dull. If it's dull, it means you've already unlocked the item and you can move on.
Don't forget to check the gates twice, once for modern sonic, once for classic.
There's roughly 150 pieces of artwork and 20 odd music tracks. Check out GAMEFAQ if you are that desperate for a list, but otherwise, do as I listed above and you'll pop this achievement shortly after you finish your last challenge. (This will net you both the "Mad Skillz" and Challenge related achievements too)