The order has been able to successfully stop all kinds of attacks from alien life forms. The important thing to remember here is that these alien creatures are not always strange looking or horrific to the human eye. There are also species that look very much like humans, but there are some species that look human and are far from human to. The giants are some of those creatures that look human from the outside, but they are the evolution of a rock formation that started to grow life within the molten lava.
What we mean by this is that giants are entirely made of melting rock inside and this happens in a cycle that never ends. They get their strength from recharging their backups inside of a volcano crater and we had to destroy several of them with high power weaponry. It was stopped with the use of nuclear warheads specially designed to be destructive at a small radius.