Can the Big Parasol tool card stop the extra damage a move could do?
As long as the Pokémon this card is attached to is in the Active Spot, prevent all effects of attacks from your opponent's Pokémon done to all of your Pokémon (Existing effects are not removed. Damage is not an effect.)
As an example of a Pokémon that does extra damage, Charizard ex's Burning Darkness attack states:
This attack does 30 more damage for each Prize Card your opponent has taken
Would Big Parasol prevent this extra damage?