Capacitor selection drives voltage fluctuation from TLV700 LDO
This seemed to be a problem with the value of the capacitor I was using after the LDO.
Below are some screenshots:
This is the LDO, using a ~4uF capacitor. Note the dips 300mV (which is HUUUGE)

And this is the LDO with the right 100nF, as pointed in the datasheet here:

This is probably the clearest 3.3V source I have seen so far. Note how it sits within 10mV.