FlipLetterCharacter[str_] := StringReplace[
    str,
    MapThread[
        #1 | #2 -> #3 &,
        {
            CharacterRange["A", "Z"],
            CharacterRange["a", "z"],
            {
                             "\:0250", "q", "\:0254", "p", "\:01dd", "\:025f",
                             "\:0183", "\:0265", "\[DotlessI]", "\:027e",
                             "\:029e", "l", "\:026f", "u", "o", "d", "b",
                             "\:0279", "s", "\:0287", "n", "\:028c", "\:028d",
                             "x", "\:028e", "z"
                   }
        }
    ]
]

For example,

In[6]:= FlipLetterCharacter["the quick brown fox jumps over the lazy dog"]
Out[6]= ʇɥǝ bnıɔʞ qɹoʍu ɟox ɾnɯds oʌǝɹ ʇɥǝ lɐzʎ poƃ

This can be used, for example, for showing answers to word games.