και καλά /σώνει και καλά

και καλά or σώνει και καλά:- I need to make a second entry since in every dictionary I have, the idiom mentioned is translated as 'at all costs'.
Will other lexilogists explain with examples this idiom since the above translation would be non-sensical in the examples cited?
Π.χ. Θέλει σώνει και καλά να έρθει [s/he wants to go at all costs!!] and και καλούα μόνο να πηδήξεις.. [you only want to screw at all costs!!]. Hahaha.

I think that the phrase is just a rather strong/emphatic version of no matter what

...
σώνω: [...] ΦΡ σώνει και καλά / καλά και σώνει, για κτ. που επιδιώκουμε με κάθε τρόπο, με πολύ μεγάλη επιμονή·
ΣYN ντε και καλά: Θέλει σώνει και καλά να φύγει.

As you can see, there's also the variation «ντε και καλά». As for its translation, "at all costs" / "at any cost" seems to me a bit too strong and I'd rather reserve it for «με κάθε τίμημα» (τίμημα is used literally and metaphorically, just like cost) or «πάση θυσία». I think Bernardina's "no matter what" would be more appropriate for this colloquial phrase.

Mind you, there's also «και καλά» which is entirely different, meaning so-called, ostensibly.

I think that "adamant" may work in some cases.

For example, depending on the wider context, Θέλει σώνει και καλά να έρθει could translate as: S/He's adamant s/he wants to come .

Just occurred to me that in general, another possible translation might be the term "hell-bent".

Good suggestions. I like hell-bent.
Perhaps even intent on may work ? ,, which I think conveys the general sense of the term.
Θέλει σώνει και καλά να έρθει : She's intent on coming.