I hastily buckled down and started searching in earnest.

Literal

I [topic-は] flustered-and searching-thing [to-に] serious-commitment [object-を] enter started.

本腰を入れる ('to put in one's real hips,' i.e., to get serious, to commit fully) is an idiom from the body-posture metaphor — settling one's hips means bracing for real effort. 慌てて ('in a fluster, hastily') adds urgency. 探し物 ('the thing being searched for') uses the nominalizing 物 on the verb stem.