I tried to keep calm, but in the end I snapped.

Literal

Calm-ly become [tried-ようとしたが], finally snap-ped became.

~ようとした ('tried to X') is the past of ~ようとする, the volitional + とする pattern. とうとう ('finally, in the end') has a nuance of reluctant eventuality — 'it finally came to that.' かっとなる ('to snap, lose one's temper') is a set phrase where かっと is a mimetic for a sudden flare-up of emotion.