How to make Arduino do High Speed I2C
I would consider going one level below the C++ object "Wire" and use their C files found here:

https://github.com/arduino/Arduino/tree/master/libraries/Wire/utility

There is a constant of interest in twi.h:

#define TWI_FREQ 100000L

And the register is set in the file twi.c like so:

// initialize twi prescaler and bit rate
  cbi(TWSR, TWPS0);
  cbi(TWSR, TWPS1);
  TWBR = ((F_CPU / TWI_FREQ) - 16) / 2;

/* twi bit rate formula from atmega128 manual pg 204
  SCL Frequency = CPU Clock Frequency / (16 + (2 * TWBR))
  note: TWBR should be 10 or higher for master mode
  It is 72 for a 16mhz Wiring board with 100kHz TWI */


Going by that comment, and without having to go into the datasheet (although I suggest that you do if you want to understand what those lines mean), it appears that the Arduino Mega (16 MHz) defaults to 100 kHz I2C clock.  Following the formula given, change the value of TWI_FREQ to achieve a desired I2C clock frequency.

However, after reading the datasheet of the Atmega, it appears to me that the fastest you can get [See edit].  Take a look at the section 24.5.2 Bit Rate Generator Unit to confirm this.  If you define "High Speed" to be 3.4 MHz I2C, then the answer appears to be no, you can't achieve that with your current hardware, but you should be able to get something faster than the default 100 kHz if you really want to.

EDIT: It may be possible to achieve 1 MHz if I'm reading the datasheet correctly.  Formula used from the datasheet: SCL = (F_CPU)/(16 + 2*TWBR*4^TWPS)  The disclaimer below still stands :p

Disclaimer: I just took a quick glance at the docs to come up with the above, it's totally possible that I missed something. Please read the datasheet to confirm any of this and familiarize yourself with your microcontroller, since you are wanting to do something that the Arduino library does not offer.