I will try my best to explain the intricate jumps I perform in my runs.

Background: Kratos can't do more than 2 jumps in any of the current games. But, through exploits and execution, speedrunners can lengthen or heighten each jump to gain much more overall height. Doing this lets the runner move out of bounds and get around triggers and save a lot of time.

God of War 1:

>> High Jump
> [Hold Triangle > Square > X]

The most basic trick in the entire game. By pressing square at the highest point of the ascension (triangle), you can jump again therefore increasing the height of your 2 jumps.

>> Apollo's Offensive Jump
> [X > L1 + X > X]

This air attack actually puts Kratos -slightly- higher, and slightly farther. This is very useful for securing basic high jumps and giving you the ability to jump out of the difficult jumps later in the game. Very useful.

>> Medusa High Jump (Blade of Artemis equipped)
> [X > R2 > Square > Circle > R2] Repeat to slowly gain height, not infinite.

The bread and butter of the God of War 1 speedrun. This makes use of the height gain Kratos receives from using Medusa's Flash (L2) while in the air, combined with the height gained from doing a square combo canceled by a circle attack. All of this done in the air.

>> LAM glitch
> [Press R2 before touching the ground]

The Lenient Air Momentum glitch. Whenever kratos does an action in the air (besides jumping), the momentum that Kratos would receive from the attack kind of "glues" to Kratos, so when he jumps again, it makes him very floaty. Using this glitch causes Kratos to gain much more height on his first jump, further lengthening Kratos' overall height gain.

>>The Fuse Glitch
> [While in the air: R2, then L1+X]

This glitch allows Kratos to switch weapons in midair, resulting in an Apollo's Offensive, which gives Kratos the ability to jump again.

>> LAM + Medusa High Jump + Fuse Glitch

> While in the air: [Press R2 before hitting the ground, X > Square > Circle > R2 > repeat > R2 > L1+X > X > Square > Circle > R2]
The most extensive jump in the game. Performing all of the above tricks will give Kratos the most amount of height. Used in a large chunk of the skips later in the game.

God of War 2:

The regular high jump from the first game was patched. Runners have found other ways to give Kratos a second jump after performing an Ascension (Hold Triangle).

>> Breakout Glitch
> [Start > O > Start] or [L2 > Start > L1 > Up > Right > Start > X]

Whenever Kratos switches weapons or turns off Poseidon's Urn, it causes Kratos to enter a neutral state, allowing him to perform a second jump.

>> High Jump (Barbarian Hammer)
> [Hold Triangle > R2 > L1 > Start > O > O > O > Start > X]

Using the breakout glitch, we can make Kratos perform a second jump after doing Might of the Kings (MotK)

>> High Jump (Poseidon's Rage)
> [Hold Triangle > L2 > Start > L1 > Up > Right > Start > X]

A safer, but slower alternative to the MotK high jump. Cannot be used without the MotK high jump to gain height. Using Poseidon's Rage and then turning off the Urn that lets you use it also creates the breakout glitch, giving Kratos another jump.

>> Higher Jump (Barbarian Hammer)
> [Hold Triangle > R2 > L1 > Start > O > O > O > Start > R2 > L1 > Start > Start > O > O > O > Start] Repeat to gain height

The first of the difficult high jump tricks. Using the breakout glitch during the MotK (L1) attack, Kratos will slightly rise during every execution of the MotK attack. Performing the breakout glitch and MotK attack causes Kratos to gain height to a limit.

>> Infinite Jump (Barbarian Hammer)
> [Hold Triangle > R2 > L1 > Start > O > O > O > Start > R2 > L1 > Start > Start > O > O > O > Start] Repeat to gain height [Breakout Glitch (Poseidon's Rage)] [Continue Barbarian Hammer Higher Jump]

So with the Higher Jump w/ the Barbarian Hammer, Kratos will steadily lose height during consecutive usage of the high jump. Using Poseidon's Rage during the jump resets the losing of height from the MotK high jump. This can be performed indefinitely to gain essentially infinite height.

>> Icarus Ascension
> [L1 + X]

Once you acquire the Icarus Wings, beginning high jumps are much easier due to being able to have the Hammer equipped before jumping.

As I run more games I will expand this list.