Short answer: Usually a 3,000 W pure sine wave inverter for a 13,500 BTU unit. With a soft-start kit, many owners run one on a 2,000 W inverter if nothing else large is on.
A 13,500 BTU AC typically runs at 1,200–1,500 W and can surge to 2,000–3,500 W when the compressor starts. A 15,000 BTU unit runs closer to 1,500–1,800 W. At 12 V, 1,400 W draws about 130 A from the battery, so wiring and fusing must be sized for it (see the wire size and fuse calculators).
Safety: These are general estimates, not a design. Follow your equipment manufacturer's instructions and local electrical code, and consult a qualified electrician for anything connected to shore power, a house, or high-current batteries.
Sometimes, with a soft start and nothing else large running. Without one, the startup surge often trips a 2,000 W inverter.
Not required, but at 24 V the current halves, so wire and fuses get smaller.
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