The Hypochondriac badge is for "Consuming 200 Medicine"
This is fairly self-explanatory. Medicine; are bottles of liquid you can chug for health. There are two kinds normal and large.
You will find them lying around pretty commonly so just keep using them as need and you will likely unlock this as you naturally progress.
Also two handy things to note:
1. The in-game badge menu tracks your progress.
2. Leaving a trial after gaining progress still counts towards it.
Video guide for reference: