2001 Nissan Pathfinder grinding sound when I am shifting

Grinding or clashing is usually caused by a clutch that is not disengaging fully. If you double pump the pedal does it change, and how does the pedal feel, particularily where the friction point is? If the clutch pedal and operation seems satisfactory, you could have internal issues as well. I would first try changing the fluid, and be certain you are putting the specified fluid in. Typically, reverse gear is not synchronized, and clashing is usually a result of the clutch.

You could try bleeding the clutch, air would most certainly create a clutch disengagement issue. Is the fluid in the reservoir low, or has the hydraulic system been opened up? I will give you the ALLDATA procedure on bleeding.
AIR BLEEDING PROCEDURE

CAUTION:

Check the clutch fluid level of the reservoir for shortage.
Keep clutch fluid away from the coating surface of the body or other parts. If it adheres, remove it quickly and flush the area with water.
Fill up master cylinder reservoir tank with new clutch fluid.

Connect a clear vinyl hose to air bleeder.
Carefully depress clutch pedal fully and release it. Repeat the cycle several times at an interval of 2 or 3 seconds.
While depressing clutch pedal, open air bleeder.
Close air bleeder.
Release clutch pedal, and wait for approx. 5 seconds.
Repeat steps 3 to 6 until no air is found in brake fluid.

Here is the capacity specs, and fluid recommendations for your trans, also a service bulletin specifying fluid requirements and NISSAN part numbers.

Manual Transmission Fluid Specifications Capacity 5.1 L
Type API GL-4, SAE 75W-90

Classification: MT02-001B

Reference: NTB03-015B

Date: December 21, 21009

2001-2010 NISSAN; MANUAL TRANSMISSION OIL REQUIRED FOR WARRANTY REPAIRS

This bulletin has been amended. Please discard all copies of the earlier version.

APPLIED VEHICLES: 2001-2010 Nissan Manual Transmission-Equipped Vehicles

SERVICE INFORMATION

If an Applied Vehicle equipped with Manual Transmission (MT) needs servicing for warranty repairs, Nissan Manual Transmission Fluid (MTF) HQ Multi 75W-85, Nissan TransElf NFJ 75W-80, or Nissan GTR R35 Special is required. See the chart above.

IMPORTANT NOTE:
Nissan Manual Transmission Fluid (MTF) HQ Multi 75W-85, Nissan TransElf NFJ 75W-80, or Nissan GTR R35 Special oil must be used when performing manual transmission repairs paid by Nissan. These include warranty, service contract, or goodwill repairs.

Nissan will not reimburse dealers for manual transmission repairs when Nissan Manual Transmission Fluid (MTF) HQ Multi 75W-85, Nissan TransElf NFJ 75W-80, or Nissan GTR R35 Special oil is not used.

Nissan recommends use of the above listed manual transmission fluids, which optimize shift quality, for customer pay use as well.

Nissan Manual Transmission Fluid and all Nissan chemicals are ordered through the Direct Ship Chemical Care Product Program.