Does having 3 Shard of Undoings and three temporary units that die kill three enemy units?

Yes, having three Shard of Undoings and three temporary units that die simultaneously will trigger the Shard of Undoing ability three times, requiring your opponent to kill three of their units.

The Reasoning

Shard of Undoing has the following ability: "The first time a friendly unit dies during your Beginning Phase each turn, each opponent must kill one of their units."

When your three temporary units die simultaneously during your Beginning Phase, the following occurs:

1. Rule 383.1.b states: "If an ability triggers 'the [Nth] time' something happens and that trigger condition is met multiple times simultaneously, the ability’s controller picks one of those instances to serve as the trigger condition. The ability triggers only once, due to the chosen condition."
2. Because the death of your three units happens simultaneously, each Shard of Undoing sees the event as a single "first time" that a friendly unit has died.
3. Each Shard of Undoing will trigger exactly once.
4. Consequently, you will have three triggered abilities on the chain. Each one, when it resolves, will require your opponent to kill one of their units.

Summary

You will receive three total "kill" triggers—one from each Shard of Undoing—because each card's "first time" condition is satisfied by the single simultaneous event of your units dying. Your opponent will be required to kill three units total, assuming they have valid units to kill for each instruction.

Note: I could not fully verify this ruling against the retrieved rules.