I've been puzzling over the meaning of this:

"Cad is féidir leat 'dhéanamh?" ars eisean.
"Do ghearrfainn adhmad go maith agus dá mbadh gábhadh, dhéanfainn céad aicillidheacht nách é," ars eisean gan cuimhneamh d'á dhruim.

I guess I get the gist:
'What can you do?' he asked.
'I could chop wood well if needed, besides, I'd have great workout' he said without thinking.

That's how I understand it. Is it more or less correct?
I have particular difficulty in understanding the parts in bold and I have no clue whatsoever about those underlined parts.

Any help appreciated.

"Gan cuimhneamh d'á dhruim" means "without a thought for his back" (the implication being that chopping wood is back breaking labour).

I'm not sure what the first part is exactly. It looks like an old spelling of "aclaíocht" which means athleticism or skillfulness. The "nách é" part is really throwing me.

Edit:

To add, what I mean is, "nách é" I assume means "that it's not" referring to something said prior. But I still can't make sense of it. He's talking about the athletic or skill based act of chopping the wood I think, but I can't figure out the point being made.

"I would do one hundred other exercises (nách é = that aren't it), he said, without thinking of his back.

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That makes sense! Is it an older rendering of aclaíocht? I didn't know that could be used for "an exercise".

A good way of saying it in English would be "and if needs be, I would do 100 other exercises besides".

Thanks a lot guys , now it makes much more sense.

But I'm still wondering why we have here "dá dhruim", shouldn't "cuimhneamh" be followed by "ar" instead of "do/de"? That's why I didn't think it could be the literal meaning i.e. "back", but rather some fixed phrase or expression (do/de + droim).

FGB gives the example "rud a chuimhneamh do dhuine", meaning "to remind someone of something", which fits with the explanation above that he's not "thinking of his back" (as opposed to "remembering his back").

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I'm not a native (or entirely fluent) speaker, so be sure to wait for confirmations/corrections, especially for tattoos.