In what sense can Sanchin be seen as containing all Goju? There's basic stance or Sanchin dachi. There's a straight punch and a closed-fist middle-level block and a grab and pull in with both hands and a push out with both open hands and a mawashi-uke. That's all of Goju? Those who say that you can find all of the techniques of Goju in Sanchin are trying on the Emperor's New Clothes.
To me, there are a few really important things in Sanchin that are often ignored or passed over. And one of the most fundamental is the position of the arms throughout most of the kata. This position--with the elbow down and the angle between the forearm and the upper arm slightly more than 90 degrees--is fundamental in Goju-ryu. Learning to maintain this position or rather to instantly move into this position--whether the hand is closed as it is in the blocking position of Sanseiru or open with a vertical hand as it is in Shisochin or open with the palm up as it is in Kururunfa--is fundamental to good technique. It's similar to the arm position one sees in T'ai Chi ward off only in Goju it is done with the elbow down. The goal should be to maintain the integrity of this structure--with ligaments, tendons, muscles, and bones all involved. Whenever the arm comes up to "block" or rather to intercept the opponent's attack, this position of the arm is assumed. It is neither too stretched out nor too collapsed--both are weak.
The second is not always practiced, but it has to do with the kata being performed very slowly, though that really has nothing to do with it--it just makes it easier to work on--and that is, one should use the whole body in a truly integrated fashion. In other words, each punch and block is moved by the core of the body or by using the koshi if you will. This should not be exaggerated, but neither should the waist or shoulders be locked into place. One should feel this movement when the fist goes out and when it is drawn back. This is practiced in Sanchin because all movements should employ the body in this fashion. To paraphrase the Chinese classics, the waist is like a millstone and the arms and legs merely follow.
So what are the three battles beginners must fight in Sanchin kata? Is it "mind, body, and spirit," as students have always been told? Isn't everything mind, body, and spirit? Perhaps it is (1) how one breathes, gathering and directing one's energy; (2) how one moves, using the koshi, with a supple waist; (3) and how one maintains the integrity or position of the body, especially the position of the arms.