The Leviathan is a ranged fight with a melee component you have to pray against anyway. The arena works against you as much as the boss does.

Getting there

Two ways in:

Teleport nexus. Find The Leviathan in the boss teleport list. The nexus shows its difficulty rating, its notable drops and any requirements before you commit.
Command. ::lev takes you straight there.

The command puts you in your own private instance and does not cost an instance token. There is no reason to fight this one in a public area.

The nexus lists The Leviathan as Master difficulty with no entry requirements, so nothing gates you but your own gear.

The melee orb

The Leviathan fires an orb that counts as a melee attack despite arriving as a projectile. If you are not praying Protect from Melee it hits for 25 to 40.

This catches people out because there is nothing in melee range. Keep Protect from Melee on even while fighting from distance.

Falling rocks

Rocks drop into the arena and deal 25 to 40 to anyone underneath. They also leave objects behind that block movement, so the arena progressively gets more cramped as the fight goes on.

What to do: keep moving and keep an eye on where the floor is filling up. Plan your movement before you are boxed in, not after.

Chip damage

A smaller repeating attack deals 5 to 11. Individually harmless, but it runs constantly alongside everything else and it is what closes the gap between a survivable hit and a fatal one.

Putting it together

Protect from Melee on, even at range.
Attack from distance.
Keep moving out of rock impacts.
Watch the arena filling with debris and reposition early.

What to bring

Ranged. The fight is at distance and you are moving constantly.
Protect from Melee. The orb is the single biggest repeating hit and it is fully prayable.
Food. Rocks plus chip damage add up steadily.
Patience with positioning. Getting boxed in by debris is the usual cause of death.