ἀνάβασιν τὴν αὐτήν does the second acc depend upon the verbal noun?
The whole sentence: ἡγήσατο δ᾽ αὐτοῖς ἀνὴρ Πέρσης δοῦλος γεγενημένος τῶν ἐν τῇ ἀκροπόλει τινὸς φρουρῶν καὶ καταμεμαθηκὼς κατάβασιν εἰς τὸν ποταμὸν καὶ ἀνάβασιν τὴν αὐτήν.
Yes, I read it as being dependant on ἀνάβασιν and almost parenthetical. He thoroughly knew the descent down to the river and the ascent back (being the same).