In a 1v1v1v1, do you need to conquer all 3 battlefields to win?

In a 1v1v1v1 (FFA4) game, you do not necessarily need to conquer all battlefields to win, but there are specific restrictions when you are attempting to score your final point.

According to Rule 466.1.b.2, when you are at 1 point away from the Victory Score (which is 8 in FFA4, per Rule 483.3), the following applies:

• If you score through Conquer: You only gain the winning point if you have scored every battlefield (via either Conquer or Hold) during that same turn. If you conquer a battlefield but have not scored every other battlefield that turn, you do not win the game; instead, you draw a card.
• If you score through Hold: You gain the winning point without needing to score other battlefields (Rule 466.1.b.1).

In summary, while you don't need to conquer all battlefields to win in general, if you are attempting to win the game by conquering a battlefield for your final point, you must have scored all battlefields in that same turn.