Note: These might be unofficial and are not yet fully confirmed. Credited to people who uploaded images/videos/information.
How to get
[Fiend Farewell] Can be used when one of your monsters is destroyed by battle. 1 random Fiend-Type monster from your Deck is sent to the graveyard.
[Compensation] Can be used each time your Life Points decreases by 1000. Send the card on the top of your Deck to the Graveyard, and recover 300 LP.
[Destiny Board] Can be used if "Dark Necrofear" is in your Graveyard, and your LP are at 2000 or below. At the end of your 5th turn after activating this skill, you win the Duel. This skill is negated if "Dark Necrofear" leaves your Graveyard. This skill can only be used once per Duel.
[Tether of Defeat] Can be used when one of the opponent's monster is destroyed in battle. The Top card from either your or the opponents deck is sent to the graveyard.
[More skills are expected.] Report Skill name and details by submitting comments or screenshot at the bottom of the page.
How to unlock Bakura
There has been no official announcement about how to unlock Yami Bakura. However, at Jump Festa 2016 that was held on December 16th-17th in Tokyo, JAPAN, visitors can play a duel against Yami Bakura, Pegasus, and Yami Marik visiting the Duel Links booth.
When Yugi's classmate Bakura was possessed by the evil spirit inside the Millennium Ring, he transformed into Yami Bakura. He is merciless and will stop at nothing to achieve his goal. Yami Bakura's Occult Deck focuses on Fiend and Zombie-Type cards.