Why this pair of IGBT's died silently?
Multiple problems. It sounds like you don't really understand HV electronics, and I suggest you stop before you get injured or worse. Your circuit is dangerous (to you, your Arduino and your computer).

Your 1N4001's are only rated to 50 V -- you should use 1N4007's if you need diodes.

You have nothing to limit inrush current when plugged in to the mains -- likely will blow the bridge rectifier also.

But - you don't need diodes to drive IGBTs. You only need the anti-parallel diodes if you are driving inductive loads (or very long wires).

The IGBTs won't turn off fast enough -- there is nothing to discharge the gate. 

You can't drive the high-side IGBTs like that. You need a level shifter.

3.3 V isn't enough to drive an IGBT. Most need 5 .. 10 V.

You don't need an H-bridge to drive an incandescent light -- just a single low-side switch. That could be an IGBT, MOSFET (need rated > 450 V for US 110 V applications, > 700 V for 220 V mains supplies), or a triac (which is commonly used, but is best with a different type of controller). 

I RECOMMEND THAT YOU STOP DOING THIS UNTIL YOU UNDERSTAND THE HAZARDS INVOLVED.