If I score to 8 on my opponent's turn with Thrill of the Hunt, do I win or do I need to conquer both on my opponent's turn?

To determine if you win the game, we must look at the rules for scoring and the conditions for the "Winning Point."

The Ruling

No, you do not win the game on your opponent’s turn.

According to Rule 323.1 and Rule 467, a player wins the game during a cleanup if they have points greater than or equal to the Victory Score and more points than any opponent. While you may reach 8 points through Thrill of the Hunt on your opponent's turn, the game only checks for a winner during a cleanup.

Furthermore, per Rule 466.1.b.2, if you are at 7 points and attempt to gain your 8th point (the Winning Point) via a Conquer, you must have scored every battlefield that turn. If you have not scored every battlefield that turn, you will draw a card instead of gaining the point.

Key Clarifications

• Conquer vs. Hold: Scoring through Thrill of the Hunt (via conquering a battlefield) is subject to the Winning Point restriction defined in Rule 466.1.b.2. This restriction requires you to have scored every battlefield that turn to successfully gain the point.
• The "Winning Point" Restriction: The restriction for gaining the 8th point through a "Conquer" is that you must have scored all battlefields in the same turn. If you have only scored one battlefield by conquering on your opponent's turn, you will not gain the 8th point.
• Timing: Even if you were to successfully gain the 8th point, the game state is checked for victory during cleanup. Because the turn is still ongoing (it is your opponent's turn), the game will not conclude until the conditions are met and the appropriate cleanup step occurs.

Summary

If you are at 7 points and use Thrill of the Hunt to conquer a battlefield on your opponent's turn, you will draw a card instead of gaining the point, because you have not conquered all battlefields that turn. You cannot win the game by conquering on an opponent's turn unless you have already scored the other battlefield earlier that same turn.