Keepin' it real 25G
All levels completed without upgrades

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This one is missable (read below for a fix though). You need to play through the entire game without upgrading Blob at all. I started my first playthrough on normal and never upgraded anything and it popped at the score tally screen after the credits. The upgrades to avoid are the ones that you have to pay for either from the Upgrades option of the main menu or from within the games levels. The store is accessed in the game at the blue question marks. So basically do not buy anything the entire game and you will be fine. Obviously, this will make the game a bit more difficult but they are pretty generous with the checkpoints so it is not completely unmanageable. It is possible to reset your upgrades from the main menu. So if you have played the first 2 levels or so and were using upgrades, you can go to the main menu, "remix" your upgrades, select none and then play through the rest of the game without them. You can then replay the earlier levels that you DID use upgrades on (as long as you remember which ones they are). The achievement will still unlock. Thanks to DeweyIsOverrated for the confirmation.

Caution: I've heard unconfirmed reports that you may not be able to obtain this on Easy. Since you start with 5 lives on Easy, that may be considered an upgrade.