Well, Imposter, the answer is indeed jynx! Though strangely enough, none of the factors you based your answer on were actually referred to in my riddle.
There is a spectre who will find The spectre is gastly
He’ll always have to level grind A black gastly will turn into a purple haunter by levelling up
While I need nothing but a trade
To make the changes he has made A black jynx will turn into a purple jynx by being traded from a gen 1 game to a gen 2 game
Though in a way, he’ll have it good
His young will mirror his childhood A purple haunter can give birth to a black gastly
Nostalgia my kid will not give A black jynx can't give birth to a black child, as jynx only have smoochum as children
For my dark past life I did live Dark refers to jynx's original black colour
If my child, their loved one betrays Smoochum evolves with love, so if a jynx evolved from a smoochum, its loved one would be its trainer
My offspring may live my past days The only way for a jynx's child to become black would be to evolve from a smoochum then be traded away, thus "betrayed" by the trainer it evolved by loving
The spectre treats me with disdain
For I can cause a spectre pain Jynx sounds like "jinx", which is another word for curse. The move curse causes damage to ghost-type users.
Congrats for guessing that toughie correctly, Imposter. Now let's see if you can stump us. *tosses the riddle ball to the Imposter*