。
I barely made it there in time.
Literal
Somehow there [to-に] arrive [purpose-のに] in-time was.
Subject is omitted — no 僕 or 私 in sight, and Japanese doesn't need one. The nominalized verb phrase 着くのに ('for the purpose of arriving / in arriving') uses のに as a purpose marker rather than the adversative 'although' のに — tense disambiguates them. 間に合う is the standard idiom for 'to be in time / to make it.'