Slowly but firmly I grabbed the door handle, took another quick glance in the room, and turned it.

firmly 是形容词 firm 的副词形式。firm 本意是"坚固的、牢固的"，引申为"坚定的、坚决的"。 firmly 表示"坚定地、稳固地"，用来修饰动词 grabbed（抓住），描述抓握门把手时的动作状态。