There were quite a few anxious times, but in the end everything worked out.

Literal

Anxious times [also-も] considerably existed [but-が] in-the-end [contrast-は] everything [subject-が] went-well.

かなり modifies あった to express frequency. 結局は uses contrastive は to set up the turning point — 'as for the final outcome.' うまくいった is the set phrase meaning 'went well.' The も after 時 adds the sense of 'there were also times when...'