Crat 395a

κινδυνεύει γὰρ τοιοῦτός τις εἶναι ὁ ‘Ἀγαμέμνων,’ οἷος ἃ δόξειεν αὐτῷ διαπονεῖσθαι καὶ καρτερεῖν τέλος ἐπιτιθεὶς τοῖς δόξασι δι᾽ ἀρετήν. This is from the edition in Perseus. How can ἃ δόξειεν αὐτῷ be explained? as relative conitional?
On the other hand, the German edition I read has οἷος ἃν δόξειεν αὐτῷ, which is optativus potentialis. I have consulted the English (Yes, for Agamemnon (admirable for remaining) is one who would resolve to toil to the end and to endure, putting the finish upon his resolution by virtue. ) and the Russian translations, both inaccurate, in my opinion. It would be more accurate to translate this sentence as following: for Agamemnon happens to be such a person, capable of taking great pains over whatever he resolves upon and of enduring, accomplishing his resolutions through virtue. This translation is based on the German edition.
If based on that of Burnet’s, it would probably be something like this: for Agamemnon happens to be such a person, capable of taking great pains if he resolves upon anything, and of enduring, accomplishing his resolutions through virtue.
Overall, the German edition is easier to follow than that of Burton.

Hmm, it’s an interesting little problem but all a bιt complicated. From your post it appears that there are two different readings in question, which involve quite different constructions, each very common in itself.
(1) οἷος δόξειεν αὐτῷ διαπονεῖσθαι
(2) οἷος ἂν δόξειεν αὐτῷ διαπονεῖσθαι
(I’m without the OCT and don’t know if they’re both attested variants here or if one of them is an emendation.)

In (1), διαπονεῖσθαι is transitive and depends directly on οἷος: “he’s the sort of person to work through what he resolves.” On this reading ἃ δόξειεν αὐτῷ is the object of the infinitive. (It’s seemingly an indefinite clause in quasi-past sequence. I find that difficult.)
See LSJ οἷος III(1) for this construction of οἷος with an infinitive.

In (2), διαπονεῖσθαι is intransitive and depends on ἂν δόξειεν αὐτῷ, which directly depends on οἷος: “such a person as would resolve to work all the way through.”
See LSJ οἷος II(1) for the construction of οἷος with a finite verb.

Your proposed translation “such a person, capable” misses the sense of the correlatives (τοιουτος … οιος). I can’t say anything about the Russian.

The characterization of his personality is based on the etymologizing of αγα-μέμνων (“very remaining,” not “admirable for remaining”). Can Plato really have meant such etymologies to be taken seriously?

Another point, a simpler one: κινδυνευει ειναι is not τυγχανει ων. It’s basically “he runs the risk of being” but is used in a much weaker idiomatic sense, as frequently in Plato, and it means “Ηe’s likely to be …” or just “Ηe’s probably the sort of person to … “