Frustratingly, you cannot track the quests you have completed in the game - so I cannot provide a complete list of quests which need to be completed in order to unlock this achievement. However, I can tell you the point it unlocks and what is not required.
The achievement unlocks after you complete Goofy's Firework Adventure quest. This is at the end of the Toontown Elections quest line which the various characters are involved in. The quests are given in Toontown which is at the top of the map.
I can confirm you do not need to have completed the "collecting" quests given by the characters. I know this because the achievement unlocked for me after the fireworks show but I still had not finished collecting Pluto's bones.