The fuel filter is located at the fuel pump, inside the fuel tank. On 2003, 2004, 2005 & 2006 Mitsubishi Outlander you can access the fuel pump without dropping the fuel tank
You will need to remove the rear seats to gain access to the pump. The seat bottom pulls up at either front center section then you can slide the seat bottom out
Once the seat is out you will see a large steel cover that is screwed to the frame. Remove this cover and the fuel pump module will be directly under the cover. Disconnect the lines and electrical and then remove the 8mm bolts holding it to the tank.
Try these on-line parts resources; www.autopartsanything.com; www.partsgeek.com; www.Rockauto.com, www.stockwiseauto.com - to list only a few.
In fact, they (RockAuto) list the replacement fuel filter from around $15.70 for your vehicle.
BECK/ARNLEY part #0433021 - or it's equivalent