In order to upgrade your plasmid to level 3, you must have enough ADAM to purchase upgraded version of your plasmid the gatherers garden. For example, you need incinerate 1, 2 & 3. Obviously to get ADAM is to harvest or defend the little sisters so you are able to purchase them. You can actually get this either in the main campaign or the Minerva's Den DLC.
1. If you are playing the main story, I believe the earliest you can buy your final upgrade is in Dionysus park. Make sure you don't spend all of your ADAM beforehand. If you wait a little further into Lamb's Stronghold, all of the plasmids are slightly cheaper.
2. In the Minerva's Den DLC, you can buy your level 3 plasmid at the second part of the game in Central Computing Operations. This way is a lot faster than the main campaign since it is only 2 main areas.
*Trick to not waste your ADAM.
Before you purchase your level 3 plasmid, save your game. Then buy your plasmid, get your achievement, then reload your save and you will still have your ADAM minus your level 3 plasmid. That way you can spend your ADAM on other things and still have your achievement.