I sometimes play Shen as an AP duelist/assassin.
Core items:
and then
. Boots are whatever you want really, but you can go without them for the most part as you have 12% MS in core items and you can get more with runes and masteries, or you could pick up
to get 6% more. Really you'll still want boots for practical purpose but you can go for
any of these as they all work well in different situations.
The idea behind this build is to let your items do the damage for you. Luden's gives 100 + .15AP magic damage, Lichbane is 75%base AD (88.5@18) + .5AP, and Hextech deals 150 + .4AP damage on the active. In total you get 338.5 + 1.05AP damage in a matter of a second if done correctly. Simply unload all of shen's offense. 220 + .6, 190 + .5, 338.5 + 1.05 = 748.5 + 2.15AP (not to mention his Ki Strike) magic damage. Just with the items you have 280AP meaning that the AP scaling would give you an extra 602 magic damage for a grand total of 1350 magic damage dealt (before resistances). You can see how this can get scary when Shen has some more AP. The great thing is that Shen would then use his W to absorb damage with .6 AP scaling as well and can stay fighting long enough to use his Q to proc his lichbane again. With Shen's Q heal, Lifesteal, and Spell Vamp, he can 1 v 1 almost any squishy. But the most hilarious thing to do is Ult an Ally and give them a 2k health shield late game. It's so satisfying.
Edit:
can be pretty good on him, but I wouldn't recommend
even if you get Rylai's. Shen doesn't have a DOT ability so I don't see him using Liandry's very effectively.