LastSuccessfullBuildWithArtifact.ps1

$env:API_TOKEN="<your_api_key>" # use secure variable in case script runs from the build
$env:APPVEYOR_ACCOUNT_NAME="your_account_name" # no need to setup in case script runs from the build (default environment variable)
$env:APPVEYOR_PROJECT_SLUG="your_project_slug" # no need to setup in case script runs from the build (default environment variable)
$env:RECORDS_NUMBER=10 # build history depth to search 

#!!! We assume that if build has artifacts, this file exist in artifacts list
$artifact_file_name = "db.zip"

$headers = @{
  "Authorization" = "Bearer $env:API_TOKEN"
  "Content-type" = "application/json"
}

$history = Invoke-RestMethod -Uri "https://ci.appveyor.com/api/projects/$env:APPVEYOR_ACCOUNT_NAME/$env:APPVEYOR_PROJECT_SLUG/history?recordsNumber=$env:RECORDS_NUMBER" -Headers $headers  -Method Get

$result = $history.builds | Where-Object {$_.status -eq "success"} | Sort-Object -Property created -Descending | Select-Object -First $env:RECORDS_NUMBER

$result | % {
  $build = Invoke-RestMethod -Uri "https://ci.appveyor.com/api/projects/$env:APPVEYOR_ACCOUNT_NAME/$env:APPVEYOR_PROJECT_SLUG/build/$($_.version)" -Headers $headers  -Method Get
  $found = $false
  foreach ($j in $build.build.jobs) { 
    if($j.artifactsCount -ne 0) {
    Write-Host "https://ci.appveyor.com/api/buildjobs/$($j.jobId)/artifacts/$artifact_file_name"    
    $found = $true
    }
  }
  if($found) {break}
}