Create in-cell dropdown with filtered range

As it stands, in Google Sheets, the only way to natively (that is, without resorting to Google Apps Script) populate drop-down lists is to use a comma-separated list, or reference a range. So in your case you would need to reproduce your filtered list somewhere in the spreadsheet (could be on a hidden sheet):

=FILTER(A2:A8;B2:B8="ANIMAL")

and then reference the range of that output in Data validation.

The ability to use a formula to generate the drop-down list directly would be a powerful feature, and has been submitted as a feature request by many (you might like to do the same: Help menu, Report an issue).

There is a solution using Google Apps Scripts.

Neat video explaining all the mechanisms involved:

• Part 1
• Part 2

Basically, by editing any cell on which your drop-down depends (e.g. Country for City list), for the related "City" cell it will automatically recalculate the range for validation data (list of possible Cities).

Copy/pasting the script here just in case it becomes unavailable (that example used makes & models of cars for dependent drop-downs):

function onEdit() {
  var tabLists = "lists";
  var tabValidation = "Main";
  var ss = SpreadsheetApp.getActiveSpreadsheet().getActiveSheet();
  var datass = SpreadsheetApp.getActiveSpreadsheet().getSheetByName(tabLists);

  var activeCell = ss.getActiveCell();

  if (activeCell.getColumn() == 1 && activeCell.getRow() > 1 && ss.getSheetName() == tabValidation){

    activeCell.offset(0, 1).clearContent().clearDataValidations();

    var makes = datass.getRange(1, 1, 1, datass.getLastColumn()).getValues();

    var makeIndex = makes[0].indexOf(activeCell.getValue()) + 1;

    if (makeIndex != 0){
        var validationRange = datass.getRange(3, makeIndex, datass.getLastRow());
        var validationRule = SpreadsheetApp.newDataValidation().requireValueInRange(validationRange).build();
        activeCell.offset(0, 1).setDataValidation(validationRule);
     }  
  }
}