The API takes an array, so just pass in multiple objects, e.g.:
curl -L -X POST 'https://app.testiny.io/api/v1/testrun/mapping/bulk/testcase:testrun?op=add_or_update' \
-H 'Content-Type: application/json' \
-H 'X-Api-Key: <API_KEY_VALUE>' \
--data-raw '[{
"ids": { "testcase_id": 1234, "testrun_id": 3 },
"mapped": { "result_status": "PASSED" }
}, {
"ids": { "testcase_id": 12345, "testrun_id": 2 },
"mapped": { "result_status": "FAILED" }
}]'
You can specify any test case and any test run, so you could also update multiple test runs in one go.
Regards,
Alex