It follows quite closely. The anime of 'Don't Bully Me, Nagatoro' mostly adheres to the manga plot with only a few minor differences that don't change the main story or character developments.
In general, the 'Don't Bully Me, Nagatoro' anime is true to the manga. It manages to capture the key elements and charm of the story. Some scenes might be tweaked for better animation or pacing, but these changes are not significant and stay in line with the manga's core.