Even if I fail, I'll try again.

Literal

By-chance fail-even-[concessive-ても], again try-[polite-ます].

またやってみます combines the everyday verb やる ('to do') with the auxiliary ~てみる ('try'), producing 'I'll try again.' The 万一+~ても shape ('even if [by chance]') frames the failure as a real but accepted possibility, and the polite ~ます keeps the resolve courteous. A staple template for expressing perseverance in the face of setback.