If I use Piercing Light and the first target gets removed like by Hidden Blade, what happens?

If you play Piercing Light and the first target is removed (for example, by Hidden Blade) before Piercing Light resolves, the second target will still take damage.

According to the rules and established FAQs for Piercing Light:

• "Then" is not a condition: The word "then" in the card text is a timing instruction, not a dependency. It does not require the first part of the effect to successfully resolve for the second part to occur.
• DAMAYC (Do As Much As You Can): As per Rule 356.3.e.11, instructions that can be partially followed are followed as much as possible. If the first target is no longer on the battlefield, that specific instruction cannot be executed, but the spell continues to resolve and will attempt to deal damage to the second target.
• Targeting: Because the targets for Piercing Light are chosen when the spell is finalized on the chain, the second target remains a valid target even if the first target is removed before resolution.

Summary of the sequence:

1. You play Piercing Light and choose two targets.
2. An opponent reacts with Hidden Blade, removing your first target.
3. When Piercing Light resolves, it attempts to deal 2 damage to the first target. Since that target is no longer on the battlefield, that instruction is ignored (Rule 356.3.e.6).
4. The spell continues to the next instruction and deals 2 damage to your second target.