Does a 2 Might unit kill two units at a Battlefield if Elder Dragon is on the board?

Yes, a 2-might unit can kill two units at a battlefield if you control Elder Dragon.

According to the Elder Dragon's ability, "Any amount of your damage is enough to kill enemy units." This effectively changes the definition of lethal damage to "any non-zero amount" for damage you are responsible for.

During the combat damage step, when you assign damage to enemy units:

1. Rule 460.2.c.3 requires that you assign "lethal damage" to a unit before moving to the next one.
2. Because Elder Dragon is on the board, 1 damage is considered "lethal" for your damage.
3. As long as your total attacking might (2) is sufficient to cover the lethal requirement for each unit (1 damage each), you can assign 1 damage to the first unit (killing it) and 1 damage to the second unit (killing it).

This interaction is confirmed by RiftJudge FAQ #8762, which states that with Elder Dragon in play, you only need to assign 1 damage to enemy units to kill them, allowing you to distribute your total might across multiple targets.