I have the following set of chords for piano. How can I tell the performer to either stress or underline specific notes in the chord (so as to show the melody), i.e. the notes on the heads of which I've marked their names?
Is there a notation technique that should do it? Should this be done by having two voices (as in Tchaikovsky's April)? In this case, the notation would become messy.
Try something like this: 
It separates out the main voice, and, by two means, shows that it is emphasised. It's also relatively neat.
Use a smaller note head for the non-melody notes. This would be easy to sight read. Or you could write an additional ossia-type line showing just the melody notes. In either case, an explanation won't hurt. If you only need it for this one measure, you can just write it out: "highlight notes such and such".
The suggestion by Patrx2 is quite neat, but here's another technique you can use to indicate this kind of voicing.
Obviously, if you are writing for (human) voices, you can simply split them onto separate staves, but if the notes are to be played by one hand on the keyboard, it is not very friendly to split them up. On the other hand, if this can be played by two hands, it is much easier to split them onto two staves, and this is the simplest way to play, too.
Without knowing for how long this layout continues, I would split into two treble clefs, with probably the melody in the lower clef to be played by the left hand. Doing it this way makes it easier to read and to play. As it's currently written, the left hand has nothing to play, while the right hand is asked to do some very unnatural things. If this pattern continues for a while, and the left hand will be otherwise occupied, then I would write the melodic notes with down stems, and the rest up, assuming that most of the melodic notes are lower than the rest of the chords.
However, I would really reconsider writing for piano this way. First, it's not very pianistic, and reads and feels like it's a literal transcription of a work written for other instrumentation, perhaps an ensemble. One solution is to move either the accompaniment or the melody to the bass clef an octave lower. Another is to invert the chords so that the melodic line is on top. As is, I'm not sure what effect you're trying to achieve. As a comparison, look at the first movement of the Beethoven Waldstein sonata, in the chorale-like chordal section where be employs a similar technique with inner voices as the melodic line. The way that's written, it's very clear what the effect is that he's looking for.
I think the neatest way to do this is almost what you did in your example: use a different style of notehead for the emphasized notes. Of course this breaks "the rules" about note lengths, but it should be obvious to most players what it means. You could add a note explaining that the "white" noteheads in the chords should be emphasized.
Incidentally, this is quite easy to do in Lilypond (if you first read and memorize the entire manual, of course!):
\relative c' {
<< { \stemUp <d g a> <a' c d> <d, a' b> <f a> }
{ \stemUp b2*1/2 f g c, }
>>
}
If it won't cause any issues with printing the score, you could use solid colored noteheads for the emphasized notes.
I'm going to go against the grain here with some tough love. If you're not the composer, then kindly disregard. The primary issue in my opinion isn't how to notate this, it's how to avoid making decisions that leave you in this position. This isn't laziness - it's good form. The composed music itself should be clear enough on its own so that the performer (and listener) knows what's happening structurally without any special devices/techniques.
My first thought would be to split the notes into treble and bass clefs. This is traditionally thought of as the treble will be the 'tune' while the bass is the 'accompaniment'. It will obviously involve a few leger lines, and possibly accentuation marks in the treble, but I can't think of a more apposite way to portray what you want played.
Or do similar with upward and downward stems. With the possibilty of octaving (?) the highlighted notes.
