For a safe and robust design, use an AC-lossy inductor (say, ferrite bead), or a non-lossy inductor with parallel resistor (maybe a few hundred ohms). After this inductor, use a tantalum like 2.2uF to 4.7uF, and in parallel with this tantalum, just at the IO pin, put that tiny 100nF MLCC in small package.
Said solution damps oscillations by providing AC loss in both the inductor, and the capacitor (the tantalum, with very well controlled ESR), and the 100nF capacitor provides minimum possible ESL right at the power pin.
Though, the analog performance of the AVR sucks anyway. Try first without any inductor. Just the 100nF at each power pin, and AVDD directly tied to VDD.