Interfacing 5V to 3V3 devices - MAX3377 damaging my board
If I understood your question and further comments to it properly, something in ATMega fries and then MCU pins, connected to the MAX3377, stop working.

It is logical to suppose that it happens due to some physical event affecting MCU pins. Most probably that MCU, at some point in time, has pin configured as output, and MAX3377 also tries to output some voltage, and MAX having better protection on the over-current than MCU. For example, MCU outputs logical 0, but MAX, for some reason thinking that it should translate from other side of its row, puts +3V3 onto the same line. Or vice versa. I can only guess, given that you soldered everything properly and there're no shortages.

Side note on the top drawing of MAX3377. Please try to avoid mirrored drawing of power supply symbol (you have 3V3 mirrored down) so that it looks like ground sign.

Conclusion: look into MCU's datasheet to see which I/O state its pins have on power on (the moment when level conflict may happen), and the sequence of port initialization to ensure that the first thing microcode does is to assign input state to input pins and output to output pins.

But in general, as The Photon advised, stop using bidirectional translators which use bias for its decision making; use unidirectionals or controlled bidirectionals (e.g. 74LVC_256 family)

Just to add: in my opinion Maxim's sheet for this device is lacking some vital information, looking more like marketing material, and I personally would not use this device in my designs, at least without close support from Maxim.