How do I solve/handle an occasional API 400 error

If you know what the correct response code is, then mute HTTP exceptions and check for it using HTTPResponse.getResponseCode(). In the example below, I assume the correct response code is 200.

function getApiData() {
  var url = "https://api.naturalresources.wales/riverlevels/v1/all?Location=4016";
  var params = {
    "contentType": "application/json",
    "headers": {"Ocp-Apim-Subscription-Key": "xxxxxxxxxxxx"},
    "muteHttpExceptions": true // Without this, you'll still get an error
  };
  var maximumAttempts = 5; // Set a limit of retry attempts to prevent an infinite loop
  var attemptCount = 0;
  do { // Execute this block
    attemptCount++; // This needs to be BEFORE the request in case of failure, otherwise it will never increment
    var response = UrlFetchApp.fetch(url, params);
  } while (response.getResponseCode() != 200 && attemptCount < maximumAttempts); // If not 200, execute the block again
  return response;
}

Alternatively, use a try...catch statement. If you use this method, you neither need to mute HTTP exceptions nor know the exact successful response code. By disabling muteHttpExceptions (it is disabled by default), the UrlFetchApp.fetch() call will throw the error that you have been seeing. We're counting on this happening, because the error will be caught and then trigger the retry attempt. This may be a preferable strategy because it would catch other errors, whereas my first approach only catches the very specific instance where the response code is not exactly 200.

function getApiData() {
  var url = "https://api.naturalresources.wales/riverlevels/v1/all?Location=4016";
  var params = {
    "contentType": "application/json",
    "headers": {"Ocp-Apim-Subscription-Key": "xxxxxxxxxxxx"}
  };
  var maximumAttempts = 5; // Set a limit of retry attempts to prevent an infinite loop
  var attemptCount = 0;
  do { // Execute this block
    var isErrored = false; // Reset to false at the start of each new iteration
    try {
      attemptCount++; // This needs to be BEFORE the request in case of failure, otherwise it will never increment
      var response = UrlFetchApp.fetch(url, params);
    } catch (err) {
      isErrored = true; // If there was an error, set to true so the script will try again
    }
  } while (isErrored && attemptCount < maximumAttempts); // If isErrored, execute the block again
  return response;
}

Just in case your not familiar the looping logic, I'm using a do...while statement, which will execute a block of code first and then check a condition to see if that code should continue to be executed.