This is unlocked by completing the game with any ending, after the last boss you are given an option to "go back in time" or "start a new journey." If you back track in time Extreme mode does not unlock, but once you start a new journey to select Extreme Mode you need to go to the Title Screen, select "options" menu, and change the difficulty from there. You can adjust it back to Normal at any time if it's too difficult for you.
Kirito Mode
After the "Mother Claudia" main quest you unlock Kirito mode. To access it you need to go to the title screen and select "start game" and select you save file. You can then choose to enter "Kirito Mode" which is a temporary mode only available between the last two main quest. Your locked in as Kirito, but the rare item drop rates are drastically increased and all the maps are accessible besides the last main mission areas. This make it easier to get some of the best guns in the game as rare drops form bosses.
Reset Stats
Reset Kits are limited, but you can actually reset any time for free. In the "Terminal Menus" where you can adjust your skill/gear sets there's a tab called "Customization Data" As long as you never save over these and leave at least one slot blank you can "load" them at anytime and you keep all your CP/SP points which you can then place however you like. Be warned if you save over a slot and select "remove customizations" the equipment will be removed but the stats you put on will be locked. You can however load a blank 1/1/1/1/1/1 stat file and save over an old one and make it a fresh slot again. If you use all 5 slots at once though reset kits are all you have left.