I agree with both steungsongkae and SpicyChick, but I think SpicyChick's choice of Khmer words are more precise on the second part. The statement "what does not destroy me makes me stronger" symbolizes our inner strength rather than physical strength. Therefore, the Khmer words "reung peung morm moun" are more in line with the English phrase. Sorry, that is my opinion.
Here is my attempt to write in Khmer.
Warning!!! I am a little rusty with my Khmer writing. So please do tell your friend to seek 2nd, 3rd, 4th...opinion before engraving these permanently on to her body...
អ្វីដែលមិនអាចបំផ្លាញខ្ញុំ បាន គឺធ្វើឲខ្ញុំកាន់តែរឹងពឹង មាំ មួន
In Khmerglish "Ahvey dael min ach bomplahn kyom barn kir tver oy kyom kann tae reung peung morm mourn".
Anyone notices any errors to my Khmer spelling please chime in.