What happens when you conquer Aspirant's Climb with Green Father and Brush the battlefield when both players are at 8 points?
If this is the first battlefield that player has scored, they'll draw 1 and the game will continue with both players at 8 points.
If you replace Aspirant's Climb with Brush via Green Father's conquer or hold effect, the Victory Score will change immediately as the passive ability of Aspirant's Climb is no longer in effect, bringing both players to the Victory Score simultaneously. Rules 323.1. and 467. define winning the game as happening during a cleanup when one player has points greater than or equal to the Victory Score and greater than any opponent. If both players are at 8 points, they have not fulfilled both requirements for winning the game. They will need to score additional points in order to win. When they do so, 466.1.b. says "when a player tries to gain a point through a Score, and their current point total is one point from the Victory Score for their Mode of Play or higher, do the following: ..." If the point is from Conquering, they will draw 1 instead of gaining the point unless they have scored each battlefield that turn. In effect, every point at or above the Victory Score becomes the final point.
323.1.1. If a player has points greater than or equal to the Victory Score, and more points than any opponent, that player wins.467.When a cleanup occurs and a player has accrued Points greater than or equal to the Victory Score for their Mode of Play, and if they have more points than any opponent, they Win the Game.