。
The shaking slowly began to weaken.
Literal
Shaking [topic-は] slowly weak-become-begin.
揺れ ('shaking / tremor,' from 揺れる) is the masu-stem nominalization. 弱くなり始める is a layered construction: 弱い + くなる ('become weak') + 始める ('begin'). Earthquake or disturbance description — common news/report register.