If the Chosen Undead saves Sif in the Chasm of the Abyss before killing Sif in Darkroot Garden, a different cutscene will play before the fight; however, this can only be done if the player places the Lordvessel in the altar through Firelink Shrine, as Artorias' ring is needed to access Kaathe. In the cutscene, Sif will recognize the player as they approach and let out a whimper. The protagonist reaches out to pet the wolf, but Sif pulls away and howls mournfully before sadly picking up Artorias' greatsword. The fight will continue as normal after this point.
For melee fighters, getting underneath Sif is generally the best strategy, as it makes most attacks miss the player character completely. Care must still be taken to dodge, block or move out of the way of the slam attack, though. Target-locking is not recommended when doing this, as it can make the camera spin and make it harder to control one's position. Two-handing is recommended, as it will make the fight shorter and reduce the number of slams that need to be dodged.
For ranged characters, simply target-lock Sif and kite Sif backwards around the edge of the arena. Try to stay as far as possible (while not losing the lock, naturally) and all of Sif's attacks will miss. Use fast attacks (ex., Great Soul Arrow, Lightning Spear, Homing Soulmass, etc.) or cast only while Sif is performing a spinning attack; Sif's other attacks are too short, and Sif will generally have time to catch up if the player tries to cast slow spells (ex., Great Heavy Soul Arrow). While not casting, keep a shield up to avoid being clipped by the tip of the sword if the distance was misjudged.
Using miracles, sorcery or pyromancy to soften Sif up before moving in with melee attacks can also prove to be effective (in case the player doesn't have enough spell charges to bring Sif's health down to zero).
Using a summoned phantom as a decoy can make positioning oneself under the wolf easier. In a party of two or more players only one should try to get under Sif, otherwise players may bump into each other when trying to dodge the slams.
Sif's attacks can be blocked, but most of them will cause a significant loss of stamina, even with a good shield. Learning Sif's attack patterns and avoiding them completely (either by dodging or simply walking out of the way) is highly recommended.
If you're having difficulty, there is a "cheap", time consuming, yet guaranteed method that can be employed. Before you enter through the fog gate, there is a broken piece of bridge of your left that can be jumped onto. This is most easily accomplished by unequipping all of your gear beforehand. After you reach the bridge there is another pile of rock resting at the top you can easily reach also through jumping. When at the top, you should get a pretty clear view of Sif. By equipping a basic bow, your arrows should barely be able to reach sif, although for only 1 damage each. The secret is to use poison arrows to wean down Sif's health. Each seven poison arrows will take down about 540 health, requiring you to expend 49 in total. In all, this process takes 15 minutes.
Sif will start visibly limping at critical health, which vastly decreases the wolf's speed and agility. Sif's moveset also changes, having less attacks and the ones remaining being much slower and having much more ending lag.
Sif also limps at critical health when summoned to assist the player with Manus.
It may be hard to summon a phantom before the battle, as Darkroot Garden is a PvP hotspot, allowing invasions.
Sif repositions the sword to a straight position, and spins around twice. Causes massive stamina damage if blocked and can kill players if the slices connect. Can be dodged by backing or rolling away before the attack is unleashed. Sif will pause afterwards, creating an opportunity for attack.
Sif will attempt to slice the player while jumping backwards and away from the player in one motion. Has little to no starting lag. Blocking it won't give the player an opportunity to attack, but will help the player survive.
Sif will do a quick chop from side to side. Good tracking and high hitbox. Possible to roll underneath it with good timing. Also does not do much damage to the stamina bar, thus it can be blocked quite easily.