Well it's not going to work off 6 volts.
According to the CREE datasheet the LED typically drops ~6.1V at 3.3 A. Assuming your FET is fully saturated you still the 3.3V being dropped by your sense resistor you will need at least a 10V supply.
Second problem: At 3.3A & 3.3V your sense resister is going to be dissipating ~10W. From your layout I would guess that you've not left space for more than a 1/4W resistor.
With a 6V available supply you probably need to be looking at 3V LED modules, and a much much smaller value for your sense resistor (I'd suggest 0.051 ohm 1/2 Watt resistor). Also if you stick with the linear design your FET is going to need a heat sink. A switching driver will be a lot more efficient but also more design work.
Also you probably don't need a 20W LED. How may Watts is the halogen bulb you are replacing? I would wager a 1 or 2 Watt LED will be plenty of light.
What a big mistake I did there, forgetting the drop voltage in the resistor...
For the 10W, I was planning to use a 20W 1 ohm resistor with aluminum shell.
The halogen bulb is a 20W 460lm one, and unfortunately I tried some conversions between lumen and candella to see if small LED would be enough, and it seems that it wont.
So I check the datasheet, and I think that I don't need more than 2.5A, which is already ~120% total flux (and the total flux is ~1500lm, so 3 times more than my actual one).
With 2.5A and a 0.05ohm 1% resistor I'd have 0.125V drop in the resistor, which is not a lot, plus at this current the voltage across the LED is 5.9V. This make 6V total, so it should be good.
Given the fact that I'd be mostly at around ~33% total flux (like the actual bulb), this is 0.03V and 0.6A, so no problem with the 6V.
The only problem I've is : I need 0.125V between the resistor, so I need 0.125V in the positive input of the opamp. To do so, is it possible to put a resistor divider in parallel with a zener? If it is, I'd need a 1:20 conversion for a 3V zener and a 1:24 conversion for a 3.3V zener.
The other option is to take off all the electrical parts of the microscope, put a new 9V power supply and use the same schematic, with a 1ohm 20W resistor (3V x 2.5A = 7.5W to dissipate).
I don't know if the LED is very sensible to the voltage, because I'm not sure the power supply of the microscope gives a stable 6V... Enough for the 6V halogen bulb to work at least...