IGBT ratings, I don't understand how this is possible
Sure, it's possible.  However, consider that the '400A@25°C' number is based on a \$T_C\$ of 25°C, not an air temperature.  \$T_C\$ is the case temperature.  At 400A, the voltage across the device, \$V_{CE(sat)}\$, can be 1.70 V.  At 400A, that's a power dissipation of 680 W.  You will need one hefty heat sink, which may not be physically possible, especially if the ambient temperature is 25°C.   

As far as the leads carrying that current, the dimensioned drawing says that they're at least 2.21 mm wide and 0.43 mm thick.  That's a cross-sectional area of about 1 square mm, equivalent to a 17-gauge wire.  My reference chart says that 100A will cause a long segment of that thickness of (circular, uninsulated) wire to melt in 30 seconds.  Of course, these leads will not be long segments, they'll be connected to heat-sinked copper planes.  But even then, that's pushing it pretty tightly.

What have you learned from this analysis? Don't trust the first page of a datasheet! You can also happily ignore any table marked "Absolute Maximum".  You're not guaranteed a functional device or an implementable design if you court these numbers.  My professors always said that these pages are compiled by the marketing department, not the engineering department.  In this case, the table you got that number from is marked "Maximum Ratings".  Don't design your device to function near these numbers.  Instead, scroll down to the characteristic graphs and standard operating parameters (the latter is not in this datasheet, but it will be in others) and design based on that.  Determine how much current your PCB or wires can handle, and how much heatsink capacity you can add, and then decide whether this type of package is even feasible. 

You mentioned that you were on Digikey; I'm guessing that you took a wrong turn and went looking for a high-current part in the 'Discrete Semiconductor Products' group, section IGBTS - single.  This section is for PCB-mounted components.  The realities of PCB manufacturing (soldering, copper thickness, heatsinking) will limit the practically achievable values here. If you want to get really high-current stuff, go to 'Semiconductor Modules', that's where the chassis-mounted parts connected to thick wires are located.  The IGBTs section there has components like this beast, shown with a pencil for scale (borrowed from Wikipedia):



That device can actually handle 3300 and 1200 A; it's 190 by 140mm rather than a little PCB-mount device.  There are plenty of smaller, more reasonable devices available as well.