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I play Tristana almost exclusively, and at this point I think probably the only enemy who offers a decent challenge solo mid is a really good Karthus. The reason why? He can easily punish you for being too aggressive.
Sivir used to be a problem for me, but she's actually really easy. All you have to do is ignore trying to farm against her and just kill her. It's that simple. ^^
At level 1-2 Harass with Explosive Shot and autoattack until she is about half-health, at level 3 Rocket Jump on her head, explosive shot, ignite, auto-attack, she's dead. Don't let her intimidate you and you'll be fine. The mistake most people make against Sivir is playing too passively and allowing her to farm/level up. No one can outfarm/outlevel Sivir, so it's foolish to let her have free reign. If she hasn't died at least once by level 6 your laning was probably a failure. Just denying her a few creeps doesn't really cut it since she can easily make up for it later.
Doran's shield is never necessary as Tristana, but it's not necessarily a bad idea. I just go with vamp scepter though, saves you money in the long run, and helps you stay in the lane if you make mistakes and take some damage.