I mustered my willpower and sprang up.

Literal

Vigorously spirit [object-を] putting-in, body [object-を] raised.

がばっと is a mimetic for a sudden, energetic physical movement — especially bolting upright from lying or sitting. 気合を入れる ('put in fighting spirit') is a set phrase for psyching oneself up. 身を起こす ('raise one's body') is the literary way to say 'sit/get up.' All subjects omitted — pure action narration.