I tripped and fell into the cesspit, and ended up soaked head-first.

Literal

Tripped [conjunctive-で] cesspit [to-に] fell, head [from-から] completely soaked [regret-てしまった].

こえだめ (肥溜め) is a cesspit for collecting human waste as fertilizer — a historical rural fixture. どっぷり is a state mimetic for being completely submerged or soaked; paired with と (here omitted) it describes total immersion. The conjunctive masu-stem 落ち (from 落ちる) chains the clauses in a written-narrative style. ~てしまった marks the outcome as regrettable.