It would be good to know, what is the function of a micro that is most affected by supply voltage ripple?
That is difficult to answer because each micro behaves differently. As a general answer:
1. if it uses an internally generated clock (NOT crystal controlled), its frequency might shift in sympathy with the instantaneous supply voltage.
1a. any peripherals using the clock may also lose timing accuracy.
2. If the ADC uses an internal reference, or uses VDD as the reference, it will scale each step from the reference and that might cause inconsistent measurement.
The logical functions should still work fine, they are quite immune from supply noise as long as the minimum voltage condition is met.
I would caution you about how you measure ripple. In practical terms, the MCU is completely unaware of its surroundings, it only sees what is on its pins. That means when you measure ripple it has to be directly between the VSS and VDD pins, not referenced to a ground somewhere else. Similarly, any analog voltage is measured across the pins, usually an input and VSS so you need to consider where the voltage drop causing the ripple actually occurs. A voltage drop generally means current is flowing through a resistance, make sure that drop isn't influencing the MCU operation.
Brian.