The connotations you see in "ajusticiamiento" come from the context, and what follows this word ("venganza", "cuerpo por cuerpo") makes them perfectly clear. There's no need to find a word in English that conveys this idea. "Ajusticiamiento" does mean "execution": judicial killing of a condemned person. That is how it should be translated. The point you want to convey is perfectly clear. The point of using the word "ajusticiamiento" is rather that it purported to be a judicial killing but actually wasn't.

"ajusticiar
1. tr. Dar muerte al reo condenado a ella."
http://lema.rae.es/drae/?val=ajusticiar

I think any other translation would actually be a mistranslation.

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Note added at 9 mins (2013-09-05 20:05:36 GMT)
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As I say, the point you must preserve is the purportedly judicial nature of this killing, not the fact that it was done in revenge, which is stated just afterwards.

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Note added at 14 mins (2013-09-05 20:10:25 GMT)
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I think this is all the more so since "execution" is also used in English with similar connotations, for criminals killing someone. "Ajusticiamiento" is used for this, but that doesn't mean that it inherently carries implications of tit-for-tat killing.

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Note added at 16 mins (2013-09-05 20:12:41 GMT)
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This "ajusticiamiento" was "en venganza". In other circumstances, the same word, applied to a murder, might signify some sort of judgement (such as Al Qaeda "executing" hostages). It means "execution", nothing more, nothing less.

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Note added at 21 mins (2013-09-05 20:17:55 GMT)
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Sorry to labour the point, but consider this too: why is "ajusticiamiento" in inverted commas? Because it expresses what this killing purported to be, not what it actually was. It purported to be execution; it was actually revenge.

And if you use a word or phrase meaning "revenge" for "ajusticiamiento", "en venganza" becomes a tautology.

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Note added at 2 hrs (2013-09-05 22:36:21 GMT)
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As for "executing someone to bring him/her to justice", that's what "execution" means:

"the act of killing a person as a punishment for a crime"
http://www.macmillandictionary.com/dictionary/american/execu...

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Note added at 4 hrs (2013-09-06 00:51:38 GMT)
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Hi Wendy,
Well, according to the Academy they are exact synonyms. "Ejecución" can mean "acción y efecto de ejecutar", and the relevant definition of "ejecutar" is: "2. tr. ajusticiar (‖ dar muerte al reo)". Perhaps "ajusticiamiento" sounds somewhat grimmer, and it's probably a bit more old-fashioned. I honestly think that all the connotations of "ajusticiamiento" are covered by "execution", which is intrinsically killing someone by judicial process, on the grounds of justice, as punishment for a crime. Many, including myself, would argue that the death penalty is always, in part, an act of retribution as well as justice.

I think we should also bear in mind that Spanish has two words, ajusticiar and ejecutar, where English has only one, execute. Although people sometimes differ markedly in their views on whether and how "ajusticiar" and "ejecutar" differ from each other (although the RAE denies that there is any difference), as can be seen this discussion, for example:
http://forum.wordreference.com/showthread.php?t=2329023
those arguments can't be applied to the relationship of "ajusticiamiento" versus "execution"; "execution" is used in various ways, but there is no other word that correctly corresponds to "ajusticiamiento". It simply doesn't mean "retribution" or "revenge killing" or anything of the kind.

The point is that Montoneros "executed" Aramburu in retaliation for Aramburu's government executing General Valle. That's the parallel, that's the exact nature of the retaliation, and it must be reflected. There's no other word in English for killing someone as the result of a death sentence.

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Note added at 5 hrs (2013-09-06 00:57:30 GMT)
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My feeling is that the writer has used "ajusticiamiento" rather than "ejecución" here in order to accentuate the supposedly "judicial" nature of the killing, because "ejecución" is quite often used as a loose synonym of "asesinato".

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Note added at 5 hrs (2013-09-06 01:00:19 GMT)
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The "crime" for which Montoneros "executed" Aramburu was precisely killing Valle. By presenting it as an execution, they were implicitly denying the legitimacy of Valle's execution (and by extension, of Aramburu's government), treating it as a murder rather than a judicial punishment.