If I use Stunfisk's "Paralyzing Crackle" attack and flip tails, do I still get to discard an Energy card from my Opponent's Active Pokemon?
No, the coin flip is for both Paralyzing the Pokemon and discarding the Energy card.
Source: Surging Sparks FAQ; TPCi Rules Team (2024-11-07)

Relevant cards

Note: All applicable cards may not be listed below.
SV8_64
SV8_64