This achievement is NOT retroactive with Title Update #8, so even if you feel like you've discarded way more than 100 Burncards for Black Market credits, you will have to start discarding cards from scratch.
To earn this achievement, you will need to discard 100 Burncards in exchange for Black Market Credits. In order to this, go to your Burn Card stash, select a card you no longer want, and press
at the same time. This will discard the card and give you Black Market Credits for it. Credit value ranges from 100 credits (common card) to 400 credits (rare card.) Once you have discarded 100 cards (common or rare; doesn't matter,) the achievement will be yours!