As of the release of Wave 2, it is now possible to get all the mini kits, though for the achievement, you only need one. Mini kit locations + required abilities are listed
(If I say completion of "X" then a Keystone is required and thus, you cannot complete the puzzle unless the keystone is in position on the in-game portal):
1: Simpson's Front Lawn (Requires Tracking Ability (Can be Hired))
2. Next Door Neighbor's House (Not Flanders) (Requires Relic Detector (Should have due to Wyldstyle) + Tow (Should have due to having to build Homer's Car) + Laser (Can be Hired))
3. Professor Frink's Virtual Chili Booth (Requires Hacking (Can be Hired))
4. Inside the Hallucination (Requires Laser (Can be Hired) + Completion of "Follow the LEGO Brick Road)
(The Next few Mini Kits Require the TARDIS from the Doctor Who level pack which cannot be hired. The station for activation is at the double decker bus found behind the area you start at after the quick cutscene. The location is kept a secret for those who haven't seen it yet.)
5. Right after using the TARDIS
6. Hacking Terminal (Should have the Doctor if you are accessing this mini kit)
7. Outside the location (Requires Technology (Don't bother hiring, the Doctor can do that) + Completion of "Follow the LEGO Brick Road")
8. Behind the Electric Door (Requires completion of "Follow the LEGO Brick Road" and either A. A Character with Electricity (I don't think you can hire this type of character) or B. Completion of "Elements of Surprise") (Nothing else in the area, so return to Homer's Journey)
9. At the Pyramid, build the statues of Itchy and Scratchy, this will open up the Locate Keystone (Complete the level "Painting the Town Black" to utilize). The rift is near a CHI puzzle. This will summon Itchy and Scratchy and open up the Mini kit on the other side of the rift. (No additional purchase required beyond just the level pack)
10. Springfield Dock, reactivate the Fruit Batman signal (Requires Portal 2 Level Pack (Specifically Chell and the Companion Cube (Cannot be Hired).