From a rummage around:
The first loss came on 25 February to 3rd Armored when the Pershing assigned to F Company 33rd Armd. Reg. was knocked out by a Tiger from about 100 yards. The first hit penetrated the turret through the coax MG port and killed both the gunner and loader. The second hit shot off the muzzle brake setting of the 90mm round in the gun and destroying the tube. The third hit glanced off the right side of the turret and knocked off the cuploa hatch which was open. The surviving crew backed away, getting the tank stuck in a pile of building debris, abandoning the tank.
This tank was nicknamed Fireball . This tank was repaired, the 90mm being replaced from one on an M 36 returning to service on 4 March 45.
One tank of the 14th Armored Battalion A Company lost one Pershing when it was struck by heavy artillery fire on 1 March 45. This tank was subsequently repaired and returned to service on 7 March.
Those are the only two losses, well sort of anyway, of Pershings in the ETO. So, one did get knocked out by a Tiger (which was subsequently destroyed in the action by other tanks present) and one by artillery fire. None got knocked out by a Nashorn, nor from the accounts I’ve read were any Nashorns encountered by Pershings.

BUT….

3rd Armored T-26E3 Pershing, serial number 25, registration number 30119835, was assigned to Company H, 3rd Battalion, 33rd Armored Regiment, Taskforce Lovelady, Combat Command B.

Pershing number 25 was knocked out on 6Mar45 from the range of 300 yards by a self-propelled German Nashorn tank destroyer during the fighting in the town of Niehl, Germany north of Cologne. The Nashorn hit Pershing number 25 with its 88mm gun on the lower left front. The armor-piercing round penetrated the armor and took a path between the driver’s legs and under the turret where it started a fire. The whole crew was able to bail out before the fire set off the ammo stowed under the turret.

Pershing number 25 suffered a completely burned out turret as a result and it was determined that it would take too long to repair. So the tank was cannibalized for parts and became the only total Pershing loss in WWII of the original shipment of 20 tanks.