// This is an impelmentation of "best effort" operation. This operation
// inserts N customers into the database. Each insert should not propagate
// any exception (I've simplified the case, so it is any Exception), but returns information of its status.
Result[] runBestEffortInserts(Session session, Customer[] customers) {
    Result[] results = new Result[customers.length];
    Transaction tx = session.beginTransaction();

    for (int i = 0; i < customers.length; i++) {
        Result result = new Result();
        try {
            // Notice that we don't want to do any refreshes from the database here, because
            // additional SELECTs would have an impact on the performance.
            session.save(customer[i]);

            // Execute a database INSERT immediately. Let's assume that this will be only one
            // INSERT (i.e. no cascade saves, no inheritance, no previously queued DML events
            // in that session).
            session.flush();

            result.setStatus(true); // Report success.
        } catch (Exception e) {
            result.setStatus(false);  // Report failure.
            result.setException(e);

            // HERE
            // But in this case, according to Hibernate we have to rollback the transaction
            // and reopen the session.
            // We don't want to abort the transaction here and start all over again because we would have to
            // iterate once more (maybe even N - 1 iterations) that in this case is not acceptable.
        }

        results[i] = result;
    }

    tx.commit(); // It should commit to the database only successful operations (best effort).

    return results;
}

...

// Operation entry result. status == true means Success, otherwise Error.
// When status is false the error attribute stores an exception.
class Result {
    private boolean status;
    private boolean Exception exception;

    ...
}