It could be read as "watashi wo korosanai mono wa watashi wo tsuyoku suru".

In fact, I had recently an occasion where I was asked to translate a similar phrase elsewhere. There the objective was "me" instead of "you" as noted, though I have no idea which is a correct version of translation from the original in German. If you try out searching the phrase in Japanese, you'd get more instances of "What does not kill me makes me stronger" than "What does not kill you makes you stronger". I think that is not strange because it's easy to understand this is a universal "you" including more subjective "me" in the definition.

As to your concern about phonetic translation in katakana, I guess you could write it as such, while I may advise this kind of classical words (or maxim, should I say) could be more naturally transcribed with a combination of hiragana/katakana/kanji (in the case of this phrase, it is kanji plus hiragana) .


HTH

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Note added at 3 hrs (2007-07-04 18:32:12 GMT)
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Well, I do not assume katakana would "not sound natural" and I believe some of other native Japanese speakers, translator or not, would consent to this first thought. I was rather talking about the visibility or legibility aspects of the language, but you may initially hear how texts written only in katakana can be awkward for Japanese people in general to read through and even make proper dinstinction between terms/phrases. Usually any Japanese texts displayed in only one writing system (katakana, hiragana or kanji) results in awkwardness while gramatical structures are identical.

Indeed, it is linguistically not very much suitable if you might prefer Japanese texts in katakana-only style. And I'm really not sure whether such display may lead to some visible beauty for non-Japanese native people. Really no idea personally. (I mean, I would not imagine what reactions we'd observe when katakana-only Japanese are viewed by some ones who know nothing about Japanese.) However, if you still would like to request of that, I may interestedly attempt. Here it is:

ワタシ ヲ コロサナイモノ ハ ワタシ ヲ ツヨク スル

I made spaces to make distinction of terms/phrases, but if the definition does not have to make any sense, you would make it no-space style.

ワタシヲコロサナイモノハワタシヲツヨクスル

Wow, it appears to me as if some alien from another planet or, if not, a mechanical message from a computer is speaking to us pretending to be Nietzsche. Funny. Have fun yourself.

Also, please refer to the first line I noted above for how you could pronounce the phrase. By the way, this translation may sound rather "literal", but I only notice those instances online and this would be probably conveying the philosopher's terms most correctly.

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Note added at 5 hrs (2007-07-04 21:07:42 GMT)
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I did not mention you made a mistake nor the katakana signs look weird in any case. It still is Japanese, however, the point is that it's not very common to write that way in a book, newspaper, magazine, personal blog, whatever.

I was not further clarifying, but hiragana, katakana and kanji have thier own specific respective usages. In the case of katakana, we usually use them to note names or nouns derived from foreign origins or languages, especially from the western world, but not restricted. You may get more detailed information here: http://en.wikipedia.org/wiki/Katakana

Cheers

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Note added at 1 day14 hrs (2007-07-06 05:55:34 GMT) Post-grading
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So you are beginning to learn something of Japanese. ; )