She gripped the rope tightly.

Literal

[topic-は] rope [object-を] firmly gripped.

しっかりと is a state mimetic for firmness, solidity, doing something properly or securely. The optional と suffix on a mimetic-adverb is common when the mimetic modifies a verb and adds a touch of formality. 握る ('to grip, grasp') describes a closed-fist hold, distinct from 持つ (more general 'hold'). The combination しっかりと握る ('grip firmly') is a vivid tactile collocation, common in physical-action narratives.