Can Piercing Light repeatedly target two units on two different battlefields for 4 damage each?

Yes, you can target two units at different battlefields with a repeated Piercing Light to deal 4 damage to each.

According to RiftJudge FAQ #1752 and FAQ #6490, Piercing Light with [Repeat] is treated as a single spell that performs its instructions twice during resolution. When you pay the [Repeat] cost, you finalize the spell and choose targets for both executions.

Here is how the damage is applied:

• First Execution: You deal 2 damage to the first chosen unit and 2 damage to the second chosen unit.
• Second Execution: You deal another 2 damage to the first chosen unit and another 2 damage to the second chosen unit.
• Total: Each unit receives a total of 4 damage.

Key details to remember:

• Targeting: As per FAQ #8481, the "other" unit restriction only applies within a single resolution of the spell's text. Because [Repeat] executes the spell's instructions a second time, you may choose the same two units again for the second instance of damage.
• Battlefields: As confirmed in FAQ #5803, the two targets do not need to be at the same battlefield; they can be at different battlefields or even in a base.
• Resolution: All damage is dealt during the resolution of the spell. There is no cleanup between the instances of damage, so both units will receive the full 4 damage before any units are checked for death (Rule 715).