If I have Milotic with the "Dew Guard" Ability in play and my opponent plays Avery, do I have to discard Pokemon from my bench until I have 3 or not?
Milotic's Dew Guard prevents all effects of your opponent's Supporters that are done to you, so you would not discard any Pokemon from your bench for the second part of Avery.
Source: TPCi Rules Team (2021-09-09)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH7_38
SWSH7_38
SWSH6_130
SWSH6_130