'Devil May Cry 4 starts off with two games modes, Human and Devil Hunter. There are in fact four additional modes:
Son of Sparda
Complete the game on the Devil Hunter difficulty. This mode changes around the enemies, introducing the harder ones like blitzs much earlier. many of the enemies also get a new attack or two, like mephistos who are much more dangerous.
Dante Must Die
The hardest real difficulty is unlocked by finishing Son of Sparda mode. This keeps the new enemies from Son of Sparda and also gives all enemies a devil trigger which activates after a certain time. Many enemies like frosts get the ability to dodge the devil bringer as well.
Heaven or Hell
This mode is slightly different. All of the enemies, including the bosses, can be killed in one hit. Yep, one hit. This is a double-edged sword, as enemies can kill you in one hit as well. This changes the dynamics of the game vastly, as little enemies like gladius and mephistos are a lot more of a threat than normal.
You do get three gold orbs though, so you can take three hits before you die. It is unlocked for finishing Son of Sparda mode.
Hell and Hell
You can probably guess what this is, just like heaven or hell mode but without the upside. This mode is Son of Sparda game mode but with the three gold orb system from heaven or hell. Enemies can kill you in one hit but they have regular health bars. This is the hardest mode of all and is unlocked by finishing Dante Must Die mode.
This is a mammoth 101 stage survival battle, you against a horde of demons against the clock. This is unlocked by completing Devil Hunter mode. You get a certain amount of time for defeating each enemy and a bonus at the end of the round. More time is awarded if your stylish rank is higher. Starts out quite simple but there is a boss level every twenty levels. Very tough.
A very worthy reward. These are obtainable by defeating Dante Must Die. The super characters have a permanent devil trigger that, once activated doesn't drain the bar. Very helpful for Hell and Hell mode or the Bloody Palace. The downside is that the final score is divided by five as a penalty.
There are six pieces of special artwork to be unlocked. They sometimes replace the title scene panning around the opera house.
History of DMC
Unlocked by completing Devil Hunter mode this a video that recaps the events of the first three Devil May Cry games. Recommended viewing for newcomers but more experienced players won't find much interest here.