How to beatTughlaq Dynastyas Mongols

Raider Elephants can handle the Keshiks without any real issues.

Even with these heavy cavalry units, you're going to need spears as the Mongols to really be able to find damage against the Raider Elephants and the Healer Elephants. Otherwise, the DPS from the Keshiks just isn't there and the healing will really hurt for you in the long run as you take bad trade after bad trade.

Against a civilization like the Tughlaq, those fishing ships are able to shoot. Even from the Mongols with their double production, it can make torching down the dock very difficult and very expensive.

You can convert Healer Elephants with a religious unit. That is a possibility. You can convert the healing elephants, make them yours.