Drain the lychee and transfer to a pitcher. Set the syrup from the can aside. It will be added later.
Press the lychees several using a muddler or whatever you can use to press the fruits, like a long wooden spoon. Press just until the juices come out from the fruits but still fleshy.
Cut unpeeled mango on each side just past the seed. Scoop the flesh using a spoon and add to the pressed lychee. Muddle several times just to extract the juices.
Cut the dalandan into half and squeeze the juices directly into the pitcher. Do not throw away the peels. It will be added back later.
Pour in the gin, simple syrup, the syrup from the lychee and water. Mix well. Add the dalandan peels and mix again.
Add some ice cubes on a tall glass and pour in the mango lychee dalandan sling to fill it. Serve with a long spoon to scoop the fruits.