A2
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Well, there's the regular way and there's the ridiculously easy way. The ridiculously easy way requires that you have learned the Hadouken technique. (Refer to another source on how to do so.) One Hadouken will immediately destroy absolutely anything, including Sigma's dog and both of Sigma's forms. Just remember with Sigma's second form, you must hit his head, within the jewel on the wolf's forehead.
If you have not learned the Hadouken, you can still beat Sigma's second form (which we'll call Sigma-2) fairly effectively. Sigma-2 is a giant wolf Reploid, but as I mentioned above, the only vulnerable part of it is Sigma's head, located within the jewel on the wolf's forehead. Even then, there are only two weapons strong enough to pierce the jewel and damage Sigma-2: the Rolling Shield and a fully-charged X Buster. Any other attack will do zero damage. Your job will be to stand on one of the wolf's paws, so that you're high enough to hit the jewel, and fire Shields or charged Busters at it.
Sigma-2 has several attacks at his disposal, and all of them are rather damaging. Pay attention to visual cues as to what attack he's about to unleash. For example, when sparks appear on the tops and bottoms of the paws, he is about to fire vertical electric beams from them make sure to not be standing on or beneath either paw when that happens. You may also see a bright flash of light extend from the wolf's shoulder. Soon thereafter, lasers will fire in columns from the top of the screen. The only safe havens during this attack are directly under the paws, but the lasers are thankfully quite slow and should give you plenty of time to react. In facty are slow enough that the first lasers to appear will disappear before the attack is over, and Sigma-2 will be forzen for the duration of the attack. Wait for the first few lasers to clear, then stand up on the open paw for a free shot at Sigma-2's exposed head.
Sigma-2's only attack that has little warning is when he smashes the ground with the wolf's paws. It is a good idea to stay in motion, and perhaps even better to spend some of your time kicking up on whichever wall. The paws are safe to stand on, except when electrified or during the laser attack, so you don't have to worry about completely avoiding them so much as not being smashed by them.
Sigma-2 has a fairly long recovery time between hits, which means that he will be flashing and cannot be harmed after you've connected. During this time, do not try to hit him again, as it will be a waste of ammunition. The Rolling Shields are much easier to deal with the the X Buster, because they do not require charging, so it is suggested that you conserve them as best you can.
Of course, you should go into the battle with all four Sub-Tanks full, so if you need to recharge, you have the option. However, you may very well find that you don't need to use more then one or, perhaps, any at all. You can also make the battle easier on yourself by using a charged Chameleon Sting to render yourself invulnerable. This will enable you to stand on the paws while they are electrified and successfully hit Sigma-2's head. (You can switch your firing weapon to Rolling Shield while the Sting is in effect.) However, during the laser attack, you will still have to wait for the laser over his head to clear before he can be attacked. Also, be careful, as you will have no indication as to when the Sting is going to wear off.
Sigma-2 is really not a terribly difficult final boss, even if he looks particularly menacing. With four Sub-Tanks and a wide arsenal at your disposal, you should have no trouble defeating him.