Find the large blue things for the parts of X's Ultimate Armor (as in the previous games in the series).

"Lava" stage: Look low for it in the first phase of the stage.
"Airplane" stage: Look in the maze-like room in the second phase of the stage.
"Computer" stage: Use the portals to reach it in the second phase of the stage.
"Jungle" stage: After the "spike" area, there will be two stone spitting rocks, one on top the other. Use these two rocks to jump up top to the left area on a tree branch to get the blue pod containing the boots.
Hint: Defeating Sigma's final form:
When Sigma's final form uses its Green Ball attacks, use Zero's Green Charged shield (hold Square). Zero will charge into Green Energy, and it will bounce the attack back to Sigma. When Sigma uses its Force Charged Punch, dash to right side then counter its attacks.