R' Avraham Schorr in HaLekach V'Ha'Libuv notes that the word chen (חן) appears six times in the Megillah - as well as in Parashas Ki Sisa. Chen is, of course, 2x29, and 6xChen=348 - שמח.
The depth in this is obvious. If all twelve Shivtei Yisroel are fulfilling their mission in this world, of combating Amalek on the 13th and the 14th, then they merit the simchah of the 14th and the 15th.
Why is the fight on the 13th and 14th? Because 13+14=27, זך, and Amalek fight the zachus of Am Yisroel. Which is mostly symbolized by the term Yehudi which is why the 27th pasuk of the Megillah is Ish Yehudi. Which is also the pasuk that alludes to the battle between Shaul and Amalek - ben Kish Ish Yemini.
Next we shall tackle the 29th pasuk in the Haftara for Shabbos Zachor....