Debug Mode is huge for new runners. It serves as a training tool that's available in every version of the game, which makes learning Jak speedrunning much easier.
The following activation code is the same for the main trilogy. (Jak 1, 2, and 3)
First part: While holding down L3, press ↑ ↑ ↓ ↓ ← → ← → X X ▢ O ▢ O
You should hear a quick sound bite play after successfully inputting the first part. This means that debug mode is half way activated. Once you hear this, release your grip on the buttons and proceed to the second part.
Second part: While holding down L3, press O ▢ O ▢ X X → ← → ← ↓ ↓ ↑ ↑
Another sound bite will play, confirming that debug mode is now fully activated.
Repeat the first section of button inputs to deactivate debug mode.