Using Lambdas since java 8:
final String[][] data = new String[][] { new String[] { "2009.07.25 20:24", "Message A" },
new String[] { "2009.07.25 20:17", "Message G" }, new String[] { "2009.07.25 20:25", "Message B" },
new String[] { "2009.07.25 20:30", "Message D" }, new String[] { "2009.07.25 20:01", "Message F" },
new String[] { "2009.07.25 21:08", "Message E" }, new String[] { "2009.07.25 19:54", "Message R" } };
String[][] out = Arrays.stream(data).sorted(Comparator.comparing(x -> x[1])).toArray(String[][]::new);
System.out.println(Arrays.deepToString(out));
[[2009.07.25 20:24, Message A], [2009.07.25 20:25, Message B], [2009.07.25 20:30, Message D], [2009.07.25 21:08, Message E], [2009.07.25 20:01, Message F], [2009.07.25 20:17, Message G], [2009.07.25 19:54, Message R]]