Some giga instruments are set up with a particular controller adjusting attack times, but ANY instrument can be configured to adjust attack time using ANY controller. Use the editor, find the attack time parameter, set it, then set the controller for changing it. Don't have it running just now, so can't give more specifics -- but it is pretty easy to do.
Though you can adjust attack time in the Giga3 real time editor, this isn't the best way to do it because whatever attack time you set will be the default for all passages playing that particular instrument.
A better and slightly more complicated way is to open the editor and open the instrument of your choice. In the instrument editor (not the real time editor, but the separate application, there is a window on the bottom right of the screen that should say ENVELOPE 1. If it doesn't use the little arrow button to call that parameter up.
Now, go to MODULATION SOURCE and assign it to a free controller, I always use control 18 for attack and release times. Now go to ATTACK MODULATION DEPTH and RELEASE MODULATION DEPTH and set those to their highest settings. Save the file.
In your sequencer, when you insert a control 18 change (or whatever controller you chose for your envelope 1 settings) your attack and release time will change. 0 means there will be no change to the envelope, the instrument will play as sampled. 127 means maximum change, i.e. the attack time and release times will be very slow.
By using this method, you can alter your attack times according to the needs of the musical phrase, and simply insert a new control change when you want to have a different attack time. The disadvantage to this is that you lose the natural attack of the instrument, so obviously the first choice is to always choose the best timbre for the passage in the first place. But this cannot always be done. Finally, you'll have to make these changes in the Giga instrument editor for every instrument you want to be responsive to this control data.