(1) Background: Biological treatment of leachate in landfill sites using anaerobic ammonium oxidation (anammox) is challenging because of the intrinsic characteristics of this complex wastewater. In this work, the scale-up and subsequent full-scale implementation of the PANAMMOX® technology (LEQUIA Research Group, Girona, Catalonia, Spain) are presented as a case study to achieve long-term nitrogen (N) removal from mature leachate mostly through a completely autotrophic pathway. (2) Methods: The treatment system consists of two sequencing batch reactors (SBRs) running in series to individually operate partial nitritation (PN) and anammox (A). Following biological treatment, physicochemical oxidation (i.e., Fenton-based process) was used to remove the remaining non-biodegradable organic matter. A cost analysis comparative was conducted in relation to the former technology used on-site for treating the leachate. (3) Results: The scale-up of the process from pilot- to full-scale was successfully achieved, finally reaching an average removal of 7.4 kg N/d. The composition of the leachate changed over time, but especially once the landfill site stopped receiving solid waste (this fact involved a marked increase in the strength of the leachate). The adjustment of the alkalinity-to-ammonium ratio before feeding PN-SBR helped to improve the N-removal efficiency. Values of conductivity above 25 mS/cm in A-SBR could negatively affect the performance of the anammox process, making it necessary to consider a dilution strategy according to the on-line monitoring of this parameter. The analysis of the operational costs showed that by implementing the PANAMMOX® technology (LEQUIA Research Group, Girona, Catalonia, Spain) in the landfill site, savings up to 32% were achievable. (4) Conclusions: Treatment of mature landfill leachate in such a two-stage PN-A system was demonstrated as feasible and economically appealing despite the complexity of this industrial wastewater. Accurate expert supervision of the process was a key factor to reaching good performances.