Short answer. You don't file a wholly separate lawsuit — you file an application for damages within the same case. If the appellate court ruled in your favor, you must apply for damages suffered during the appeal by filing that application with the appellate court itself, with notice to the attaching party, before its judgment becomes executory.
What the law says
he must claim damages sustained during the pendency of the appeal by filing an application in the appellate court, with notice to the party in whose favor the attachment was issued or his surety or sureties, before the judgment of the appellate court becomes executory
Rule 57, Section 20 — Claim for damages on account of improper, irregular or excessive attachment. Read the full provision →
One case, not two lawsuits
Rule 57, Section 20 treats damages from a wrongful, irregular, or excessive attachment as part of the same action, not a separate lawsuit. Before trial, before the appeal is perfected, or before the judgment becomes executory, the party who suffered the attachment applies for damages within that same case, with notice to the party who obtained the attachment and to the surety on the attachment bond. The application must set out the facts showing the right to damages and state the amount claimed, and it is heard and decided as part of that case rather than filed as an independent complaint.
Damages sustained while the appeal was pending
If the trial court's decision goes to appeal and the appellate court ultimately rules in favor of the party whose property was attached, that party has a separate window to recover for the harm caused specifically during the appeal itself. The rule requires the application to be filed in the appellate court, with notice to the party who benefited from the attachment or that party's surety, and it must be filed before the appellate court's own judgment becomes executory. So the application is not filed back in the trial court by default — it goes to the same appellate court that just decided the case, though that court has the option of directing the trial court to hear and decide it instead.
What the application must show, and what happens after
Because this is an application for damages within a pending case rather than a new lawsuit, it still has to be proven — a hearing is required before any award is made. The claimant must set out the facts supporting the right to damages, such as losses from being deprived of the property, and state the amount being sought. Once granted, the award is included in the judgment. If the bond posted by the attaching party or the deposit given turns out to be insufficient to cover the damages awarded, the rule allows the aggrieved party to recover the shortfall from the attaching party's own non-exempt property in that same action, without having to file yet another suit.