So far, you’ve been able to break any attack after an opener, including auto-doubles, manuals, linkers, and sometimes even enders if your opponent messes up. As you would expect, you can also combo break shadow linkers, but there’s a bit more to it than just pressing two buttons.
In order to combo break a shadow linker, you must break any 3 hits of a shadow move by pressing any strength breaker (for example, MP+MK) in rhythm with the hits of your choice. It has a very distinct feel to parrying multi-hit moves in games like SFIII: 3rd Strike, and like parrying, you need to know the timing for each individual shadow move to successfully break it. You must press the buttons during each strike’s active frames, and there are gaps between the hits that will cause lockouts if you have poor timing. I personally find breaking shadow linkers to be a lot of fun, and anyone who enjoys parrying attacks will get a lot of satisfaction out of this little rhythm minigame.
Your character will flash white with each successful parry, and the announcer will shout “1, 2, 3!” as you break each hit. The timing to break a shadow linker might be slow and deliberate (Jago’s shadow Laser Sword), or as fast as you can press the buttons (Glacius’s shadow Cold Shoulder), although most shadow linkers will fall somewhere in the middle and require a decently fast-paced but not mashy rhythm to break. It helps to go into training mode and practice breaking the moves with “average timing”, such as Sabrewulf's shadow Ragged Edge and Spinal's shadow Soul Sword, since this rhythm is common to several shadow linkers. Some shadow linkers will have staggered timing, like Orchid’s shadow Flick Flack and Maya’s shadow Tumble Kick, and you’ll just have to practice these few exceptions individually. For an exhaustive breakdown on the timings to break every shadow linker in the game, including a tool that lets you practice breaking all shadow linkers in your browser, see my shadow linker break trainer.
Because the announcer shouts as you parry each individual hit, you give away your intention to break the shadow linker to the offensive player before you succeed, who might in turn decide to counter break one of your attempts. They will be successful if they hit any of your three attempts, not just the final hit which causes the actual combo break. This leads to a very interesting game of chicken with slower shadow linkers, where the offense can react to the announcer’s voice. The defense, for example, may choose to break only one or two of the hits trying to bait a counter breaker attempt. The offense may just let the shadow linker rock and dare you to break it (and capitalize with huge damage if you lock out), or he might try to intercept your mind game by counter breaking one of the earlier parries, rather than wait for the third one. There are several short mind games that can take place here, especially in a long set between players, and breaking a shadow linker is usually an exciting turning point in a match.