(Riku vs Ansem: Final Battle; Kingdom Hearts: Chain of Memories [No HP Boosts])
Ignore Riku's HP bar in this image, as I'm going to be discussing fighting Ansem without having taken any HP boosts during level ups. For those of you who do not know what that means, it means Riku would have an HP bar roughly a fourth of the size of the green one. In comparison, Ansem has four bars of HP, tied with Marluxia for most boss HP in the game (unless you count the scythes in the final battle with Marluxia, in which case he would have close to six bars).
So why is this fight so difficult? For one thing, normal Riku sucks. You need to get in a fair number of hits before transforming if you've been increasing your Dark Power during level up (which is assumed since Attack has a maximum capacity and for purposes of a no-HP challenge you won't have the option of boosting HP). Normal Riku is weak and has no mobility. He also cannot use combo sleights (not that that matters in this fight, but I'll expound on that later). This means that while you're normal Riku your number one priority is to transform into Dark Riku, through card breaks, dealing damage, or taking damage. And you're likely to be taking a bit of damage. Ansem can take Riku out in four or five hits (fewer if he nails you with a sleight). Guardian's strike is easily dodgeable by jumping and is linked to Ansem's blue (magic) cards. The shockwaves (orange, physical wth), however, are a different story. If Ansem is in the middle of the screen the only way you're going to avoid getting hit is by a double-jump-backflip (which you can't do in normal form) or breaking Ansem's card (not always possible). You have a relatively small margin of error and limited time. Careful management of your cards until you can transform into Dark Riku is the only way you'll survive.
And that brings up the next issue: Time. The longer this fight drags out, the more likely it is that you will lose. Riku has no recovery outside of Oogie Boogie (who you don't want to activate if you can avoid it since that means giving up an active Maleficent) save for Mickey Mouse, whose cards are often far lower than Ansem's in value, forcing you to sleight them in order to get the recovery effect off. Which of course leaves you screwed if Ansem uses a 0 card or a stronger sleight (likely). And that's another main difficulty: Ansem's ability card is Sleightblind. You can't see if he's holding a sleight or what cards he loads into the sleight. This is obviously problematic since most of the time you can prepare for a sleight by being ready to switch to the 0 card immediately. Not so with Sleightblind in effect. If you're caught mid-combo you lose a few precious seconds, which might be enough for Ansem to OHKO with Rockbreaker or something if your health is low enough. Dark Ascension (I might not be remembering this name correctly) isn't a problem if you can get the dodge timing down though, so use it as a chance to reload your deck if he uses it. At any rate, Sleightblind is a real problem, so you want to break it with Parasite Cage as soon as you can. The problem is, Ansem usually activates it while you're still Normal Riku and unable to dodge effectively. He doesn't do it immediately either. In most cases you'll want to activate Maleficent immediately instead in order to transform as quickly as possible. Delaying this can cause you to take dangerous amounts of damage, which hurts you in the long run.
As for your attack options, don't even think about trying sleights. The Guardian is an absolute cockblock. Most of the time it will block Dark Firaga, and you'll get maybe one hit in on Ansem from Dark Aura or Dark Break. It also prevents the three-hit stun combo from being effective. This means that your best bet to deal quick damage is the backflip downstrike, which gets in three or so hits per card. Definitely your most effective way of dealing damage, especially with Maleficent active (which it should be). The Guardian can still occasionally block this though, and if Ansem is facing away from you when you flip over him the Guardian will be in a position to block your downstrike, so don't pull the trigger too early.
Really it comes down to a combination of speed and luck. The Ansem fight is a bit of a crapshoot, so your best bet is to activate Maleficent, transform ASAP, and continuously downstrike him until he dies. Use the Mickey Miracle Sleight when you can, but for the most part you're going to have to make do with the measly HP you start the battle with.
So why is this fight so difficult? For one thing, normal Riku sucks. You need to get in a fair number of hits before transforming if you've been increasing your Dark Power during level up (which is assumed since Attack has a maximum capacity and for purposes of a no-HP challenge you won't have the option of boosting HP). Normal Riku is weak and has no mobility. He also cannot use combo sleights (not that that matters in this fight, but I'll expound on that later). This means that while you're normal Riku your number one priority is to transform into Dark Riku, through card breaks, dealing damage, or taking damage. And you're likely to be taking a bit of damage. Ansem can take Riku out in four or five hits (fewer if he nails you with a sleight). Guardian's strike is easily dodgeable by jumping and is linked to Ansem's blue (magic) cards. The shockwaves (orange, physical wth), however, are a different story. If Ansem is in the middle of the screen the only way you're going to avoid getting hit is by a double-jump-backflip (which you can't do in normal form) or breaking Ansem's card (not always possible). You have a relatively small margin of error and limited time. Careful management of your cards until you can transform into Dark Riku is the only way you'll survive.
And that brings up the next issue: Time. The longer this fight drags out, the more likely it is that you will lose. Riku has no recovery outside of Oogie Boogie (who you don't want to activate if you can avoid it since that means giving up an active Maleficent) save for Mickey Mouse, whose cards are often far lower than Ansem's in value, forcing you to sleight them in order to get the recovery effect off. Which of course leaves you screwed if Ansem uses a 0 card or a stronger sleight (likely). And that's another main difficulty: Ansem's ability card is Sleightblind. You can't see if he's holding a sleight or what cards he loads into the sleight. This is obviously problematic since most of the time you can prepare for a sleight by being ready to switch to the 0 card immediately. Not so with Sleightblind in effect. If you're caught mid-combo you lose a few precious seconds, which might be enough for Ansem to OHKO with Rockbreaker or something if your health is low enough. Dark Ascension (I might not be remembering this name correctly) isn't a problem if you can get the dodge timing down though, so use it as a chance to reload your deck if he uses it. At any rate, Sleightblind is a real problem, so you want to break it with Parasite Cage as soon as you can. The problem is, Ansem usually activates it while you're still Normal Riku and unable to dodge effectively. He doesn't do it immediately either. In most cases you'll want to activate Maleficent immediately instead in order to transform as quickly as possible. Delaying this can cause you to take dangerous amounts of damage, which hurts you in the long run.
As for your attack options, don't even think about trying sleights. The Guardian is an absolute cockblock. Most of the time it will block Dark Firaga, and you'll get maybe one hit in on Ansem from Dark Aura or Dark Break. It also prevents the three-hit stun combo from being effective. This means that your best bet to deal quick damage is the backflip downstrike, which gets in three or so hits per card. Definitely your most effective way of dealing damage, especially with Maleficent active (which it should be). The Guardian can still occasionally block this though, and if Ansem is facing away from you when you flip over him the Guardian will be in a position to block your downstrike, so don't pull the trigger too early.
Really it comes down to a combination of speed and luck. The Ansem fight is a bit of a crapshoot, so your best bet is to activate Maleficent, transform ASAP, and continuously downstrike him until he dies. Use the Mickey Miracle Sleight when you can, but for the most part you're going to have to make do with the measly HP you start the battle with.