"How is this possible? How was he able to kill those monsters on the 4th floor? Was he able to reach the soldier grade?"
Even Maria's husband or you can say the grandfather of David was surprised when he saw David killing those Monsters inside the fourth floor. Not only that it looks like he also did not have that much trouble to kill those Monsters.
You should know that he was the person who expelled David from the family due to him losing the Zen core and did not have the talent to become a guardian. But currently, if you look at the big screen then you can see most of the students who are from the Kyler family are present on the third floor while only 5 of them are present on the fourth floor and David is one of them.