Dingo_Dile

Ewww.... You guys are sick, seriously! There could be younger audiences reading that for all you know. Anyway, for the answer that doesn't involve any of the above. You need to fill either the gauge on the left of the screen (Dark Gauge, will grant you Chaos Blast when full) or the gauge on the right of the screen (Hero Gauge, will grant you Chaos Control when full).

To fill the Dark Gauge, defeat GUN soliders, destory scenery, basically, just wreck havoc.

To fill the Hero Gauge, defeat Black Arms (sometimes Eggman's robots count too), put out fires and destroy the red fruits, basically, help the planet.

When either gauge is filled, you'll hear Shadow either say
'Behold the Ultimate Power' - Chaos Control or
'Death to all who oppose me' - Chaos Blast

When you hear him say either of them, press triangle to activate the move.

gogeta ssj4

When your blue bar is full press triangle to do chaos control and when your red bar is full press triangle to do chaos blast.

Tyranitar Master

Fill your Hero guage by destroying Black Arms or Eggman's robots, destoying poisinus plants and fire. Fill your Dark guage by destroying GUN (Sometimes Eggman's robots) and destroying nature. If you here Shadow say,"Behold the ultimate power." Press triangle to use Chaos Control. If you hear him say,"Hrrrr... Death to all who oppose me." Press triangle to use Chaos Blast.