Student or Learner
From the beginning, I was relentlessly mocked by failure. In all this madness, I felt as though I were bound, gagged, and thrown into the sea! One probable solution, taking stock and calling it quits, had been eluding me from the start, but I was adamant to soldier on.
How does this combination of words sound?
Overall, you are using too many figures of speech.
You personify failure by saying it mocks you.
You are figuratively bound and gagged and thrown into a sea of something. (I don't know what you mean by this.)
If the very idea of quitting was eluding you, you can't really say you were adamant about soldiering on. Either it never occurred to you to quit, or others suggested you quit, but you insisted on "soldiering" (another figure of speech) on.
From the beginning, it was hard going. There were times when I certainly felt beat up by failure, when I didn't think I'd ever achieve my dreams. But through it all, I never considered quitting.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.