Can my opponent conquer with Adaptatron at the same battlefield twice, assuming he used Ride the Wind. Would this allow them to remove 2 gear and only get 1 point?

No, your opponent cannot trigger Adaptatron's ability twice at the same battlefield in a single turn, nor can they remove two gears in this manner.

Here is the breakdown of why this interaction does not allow for multiple triggers or multiple gear removals:

1. Scoring and Conquering are Limited

According to Rule 465, a player may only "Score" each battlefield once per turn. Since conquering is a method of scoring (Rule 464.1), you cannot conquer a battlefield that you have already scored during that turn cycle. Even if your opponent uses Ride the Wind to move Adaptatron off and back onto the same battlefield, they have already fulfilled the scoring requirement for that battlefield for the turn.

2. Conquer Abilities are Linked to Scoring

Rule 466.2.c explicitly states: "Conquer abilities trigger at a Battlefield that was Conquered... These will only trigger when the Battlefield is Scored; I.E. These cannot be triggered more than once per turn for a player."

Because the "Conquer" action only counts as a successful conquer when establishing control of a battlefield that hasn't been scored yet that turn, a second attempt to "conquer" at the same location fails to meet the trigger condition. Consequently, Adaptatron’s ability will not trigger a second time, and the opponent cannot remove a second gear.

3. The Sequence

• First Move/Conquer: When your opponent first wins a showdown at a battlefield and establishes control, they perform the "Conquer" action. At this point, the battlefield is scored, and Adaptatron's ability triggers. They may choose to kill one gear to buff Adaptatron.
• Subsequent "Moves": If your opponent uses Ride the Wind to move Adaptatron again (either moving off and back on, or moving to a battlefield already scored), this does not count as a new "Conquer" action. Because they cannot perform a second conquer at that battlefield, the condition for Adaptatron's ability ("When I conquer") is never met a second time.

Summary: Your opponent can only trigger Adaptatron’s "When I conquer" ability once per battlefield per turn. They cannot use Ride the Wind to force a second conquer or remove additional gear at the same battlefield.