You can get a replay of the last match you played:
1) At the top of the chat pane on the right, click Replay.
2) Copy the entire red text.
3) Click the Custom button in the bottom middle of the main area.
4) Paste the text in the top right of the new screen (in the field that says "Replay").
5) Click the Replay button above the text field, and enjoy!
You can also paste the replay into a text file for later enjoying.
Both your and your opponent's deck lists are included in the replay text. Look for
"deck":"<deck code>".
Also, going by the Head Hunter bonus you defeated (what was at the time) the top 1 arena deck.
You can find the deck you beat by looking at the leaderboard and clicking the name of the deck's owner. Going by the Hand Drill you won, I'm guessing you beat Regyptic's deck:
https://etg.dek.im/deck.htm#055s7025sd035rk0b5uk065um015uq055vg025ul018ps