The heart meter shows a maximum of three hit points, but Jak can technically have a maximum of four hit points by collecting 50 Green Eco pieces while at full health. As soon as you take damage, the 50 pieces will be transformed into an additional hit point (just like if they were collected at less than max health), meaning you can still take three more hits before dying!
Even if you die, the penalties are few. There are no extra lives to worry about, and no progress (excluding progress in a boss battle and clearing an area of enemies) is lost. All your collectibles and tasks will be safe, though you may respawn at a checkpoint somewhat far from where you died. Because of the minimal penalties, it may be wise to die on purpose at times to quickly respawn at a more favorable location or to top off your health before a difficult part of the game.
While killing lurkers gives you Green Eco pieces that can heal you when enough are collected, sometimes it's best to just avoid enemies entirely. You don't get XP or currency or any other incentive like that for killing enemies, so you may actually end up with a net loss when fighting enemies for health if you're not careful.
While the various colored Ecos have specific primary uses that you'll be required to use throughout the game, don't forget their handy secondary uses! Blue Eco automatically breaks open nearby containers and will cause Green Eco, Blue Eco, Precursor Orbs, and Scout Flies to home in on Jak for easier collection. Red Eco protects Jak from the harmful effects of explosive Dark Eco boxes. Yellow Eco can be more precisely aimed by entering the first-person view mode (Triangle toggles it).
While you are not required to collect every last Precursor Orb, Power Cell, and Scout Fly in a given area to progress to the next hub, it'd still be wise to collect as many as you can initially as further challenges and requirements only get more difficult and more strict. For instance, you must have a minimum of 72 of the game's 101 Power Cells to unlock the final level, so it doesn't make sense to skip all that many since you need roughly three-fourths of all of them to barely finish the game.
However, judicious collection of as many Power Cells as possible in the areas you do visit will allow you to skip levels you might not like if you're not going for 100% completion. For instance, if you've collected everything possible up to that point, the addition of trading Orbs for Cells from Gordy and Willard in the Volcanic Crater will give you enough Power Cells to completely skip Spider Cave and Snowy Mountain in that hub area.
Uppercuts (Square then X) are useful for harming hanging enemies like jungle snakes and cave spiders.
When falling from a great height, Jak may take damage upon colliding with the ground. In order to avoid this, you can exploit his gliding spin (Circle button when in the air) to slow his vertical speed a bit before he hits the ground. If timed right, this exploit will completely negate falling damage and allow you to take shortcuts that would otherwise be detrimental or deadly.
It would be wise to master the rolling jump technique (while running, hold R1 and press X after a short roll to jump farther and faster than normal walking or jumping). Besides being necessary a few times throughout the game, it's fast, can harm enemies (just like a punch or spin), and can be useful for easier access to certain platforms.
Be on the lookout for shortcuts! There are many places in the game where a more complicated move (e.g. rolling jump, double jump and hovering spin, high jump) can shorten your travel time or help you avoid enemies.
Each of the Sage huts you visit in the game have a teleporter that can help you quickly travel to previous hubs, or even to Geyser Rock if you didn't fully complete it at the beginning of the game.