Even if I fail, I'll try again.

Literal

By-chance fail-even-[concessive-ても], I [topic-は] once-more try [probably-でしょう].

万一 ('one in ten thousand, just in case') paired with the concessive ~ても creates a 'even if (the unlikely thing) happens' contingency. ~てみる ('try doing') here in volitional-future form やってみる ('try to do it') frames the speaker's resolve to keep attempting. でしょう adds a politely hedged 'probably,' which softens the assertion into a reflective declaration.