Presenting a UIAlertController properly on an iPad using iOS 8

You can present a UIAlertController from a popover by using UIPopoverPresentationController.

In Obj-C:

UIViewController *self; // code assumes you're in a view controller
UIButton *button; // the button you want to show the popup sheet from

UIAlertController *alertController;
UIAlertAction *destroyAction;
UIAlertAction *otherAction;

alertController = [UIAlertController alertControllerWithTitle:nil
                                                      message:nil
                           preferredStyle:UIAlertControllerStyleActionSheet];
destroyAction = [UIAlertAction actionWithTitle:@"Remove All Data"
                                         style:UIAlertActionStyleDestructive
                                       handler:^(UIAlertAction *action) {
                                           // do destructive stuff here
                                       }];
otherAction = [UIAlertAction actionWithTitle:@"Blah"
                                       style:UIAlertActionStyleDefault
                                     handler:^(UIAlertAction *action) {
                                         // do something here
                                     }];
// note: you can control the order buttons are shown, unlike UIActionSheet
[alertController addAction:destroyAction];
[alertController addAction:otherAction];
[alertController setModalPresentationStyle:UIModalPresentationPopover];

UIPopoverPresentationController *popPresenter = [alertController 
                                              popoverPresentationController];
popPresenter.sourceView = button;
popPresenter.sourceRect = button.bounds;
[self presentViewController:alertController animated:YES completion:nil];

Editing for Swift 4.2, though there are many blogs available for the same but it may save your time to go and search for them.

if let popoverController = yourAlert.popoverPresentationController {
    popoverController.sourceView = self.view //to set the source of your alert
    popoverController.sourceRect = CGRect(x: self.view.bounds.midX, y: self.view.bounds.midY, width: 0, height: 0) // you can set this as per your requirement.
    popoverController.permittedArrowDirections = [] //to hide the arrow of any particular direction
}