This video begins Misty Island and covers some of its collectibles (including the Muse).
If you're having trouble catching the Muse, I have two bits of advice. One, consider using the seesaw launcher to your advantage. If you time it just right, you can catch the Muse as she scurries up the steps by landing on top of her from a launch. Two, make heavy use of rolling jumps on straightaways. These are your best bet for surpassing her speed.
After catching the Muse, I clumsily headed in the wrong direction (can you tell its been years since I've played this?), but the footage was short, so I just sped through it.
If you die during the ambush (as I did, hence the transition), I forgive you. It's not too bad, of course, but I consider this the first point in the game where you genuinely have a risk of dying if you don't play it smart. Unfortunately, smarts won't necessarily save you, as luck is a factor in your Red Eco spawns. It's possible that Naughty Dog made this section a little easier by decreasing the reliance on luck (or perhaps I just had a fair string of it in this recording), as I distinctly recall this sequence being noticeably more difficult in the PS2 version. I also think I recall the cannon being more capable of hitting the metal boxes whilst still controlled by the Lurker.
Argh, if only I didn't take that turn at 8:17, I would've saved myself so much frustration later. Though you'll see me go down there eventually to wrap up Misty Island, note that the beach there has three Precursor Orbs. It's slightly difficult to tell (hence why I went on my merry way for the time being), but the presence of a Lurker on that beach (when there aren't any on the beach you arrived at) indicates that it IS a different area and not the similar-looking previous one. Misty Island is the first level in the game that I consider difficult, and another one of the reasons for that is that it has few landmarks to distinguish where you've been and where you need to go. Sure, the Precursor Silo and the whole ship & Zoomer area is pretty distinct, but the rest of it is just murky gray and brown rocks, and it's easy to get lost.
This video wraps up the remaining collectibles on Misty Island (including all of the ones in the Zoomer area). The video ends right after returning the Muse, with the intent of wrapping up the last (and now unlocked, after the Forbidden Jungle) area of Sentinel Beach before proceeding to Fire Canyon.
Definitely not a fan of the rolling barrels part of Misty Island. It is possible to get through it mostly unscathed by maintaining forward momentum without ever stopping to go on the side paths, but then you're missing out on collectibles. Additionally, that strategy isn't flawless even if you just wanted to go on the main path as it seems the barrels move just slightly faster than you at full speed, which means that you're likely to get hit by the bouncing barrels at least once if you never ever stop to recalibrate.
If you're weren't aware, you can exploit Jak's spinning glide move to prevent, or at least mitigate, the damage you'd receive from falling too high by slowing your vertical velocity. It's, of course, not realistic in the least, but it is a handy (and very well known) method for speeding up the game at points.
The Zoomer is one of my favorite vehicles in Jak II, but I don't like it that much in the first game because you're very frequently expected to make precise movements in confined spaces, and that's exactly the opposite of what the vehicle is good at. It works loads better in the comparatively open and freeform areas of Jak II.
8:00 - Warp speed activated! That significantly sped up segment should you give you some idea of how thoroughly I searched Misty Island before finally returning to the aforementioned overlooked beach.
Bonus: Misty Island Bit
This very short video covers something I've always wanted to try on Misty Island.
During the Zoomer portion of this level, one of your tasks is to ram all the balloon lurkers. After doing so, a Power Cell appears in the interior of the ship. As the subsequent audio log shows, you're really meant to take it whilst on your Zoomer (after all, that'd be easiest), but nothing stops you from dropping down to the interior and picking it up on foot. Sadly, nothing special happens. I had always hoped the game would crash or glitch out or something (as I think this is the only Zoomer-related Power Cell in the entire game that can be picked up on foot), but it seems the Power Cell programming and animations are general enough to handle this case (at least for the PS3 version).
Disappointing, but I'll also leave you with one more interesting tidbit. When creating bridges from the large bones around Misty Island, it normally takes three attacks to bring down each bone. However, if you're powered up with Red Eco, a single attack will be strong enough to cause the bone to fall. Again, nothing too special, but I just thought it was interesting that they took that possibility into account.