Here is the full list of all 18 Destiny Duel achievements.
Play 1 ranked game
Play 5 ranked games
Play 10 ranked games
Play 25 ranked games
Play 100 ranked games
Win 25 ranked games
Win 100 ranked games
Reach Iron or higher
Reach Bronze or higher
Reach Silver or higher
Reach Gold or higher
Reach Diamond or higher
Reach Arcane or higher
Reach Master or higher
Reach Legend or higher
Reach Divine or higher
Reach Immortal
Get over 100 DP as Immortal 3