It's true that Assassin's skill is extraordinary, even among servants. Saber defeated him, but also had remarkable skill AND a form of precog, and that's precisely why Suzune can't get an easy win on this duel (and why he would stomp her if he knew her weak point). Assassin will hit her way more than she can hit him (and his luck could allow him to avoid one fatal blow). So the skill gap definitively exist, but even with that, mid regen could be called a greater advantage, and based on above, she could reach Mountain Level. Assassin can handle people stronger than him, but Saber as Shirou's servant is still At Least 7-B, and not 7-A without excalibur. If Suzune can reach mountain level, she's essentially in berserker tier, and Assassin can barely redirect his blows, being clearly unable to defeat him. So, if the AP gap is that large between Kojirou and amped Suzune, i won't bet on him, as skill have clear limitations. Of course, i don't know how fast she could reach this level. It is possible that Assassin hit the soul gem without knowing it's importance, considering the necklace is totally exposed. But it's not likely to happen... Even if we talk about supernatural beings, slashing (and not thrusting, which is another story) toward the chest isn't a good strategy in a sword duel, because the ribs could prevent you from reaching the vitals. And Assassin himself seems to prefer attacking vulnerable spots like the neck... So him slashing toward the necklace is pretty much speculation. Even if you can see saber's armor reform toward the chest area in her first duel agains't assassin, it's due to her dodging Tsubame Gaeshi, not Assassin intending to hit that area. Of course, Suzune could lost her soul gem, trying to dodge that same hit... I just think it's, again, too much of a speculation.
