Hall current sensor noise
It seems you have 50 Hz noise entering the circuit. The 20ms period tell me that.
You should post a schematic of how is the sensor connected to your circuit. The Allegro has an output impedance of 1.8kOhm which is not very low so the wiring should be very short since it seems that your module has no buffer amplifier. Try with a piece of shielded wire and see if it gets better.
Alse the LTC converter has a sampling capacitor and an input impedance model that are quite susceptible to loading. Read carefully page 26 of the datasheet, even attaching the scope probe could load it.