This is my 3rd attempt on this game. For conditions of "full completion" as defined in The Legend of Zelda, see this: #7565: chatterbox's NES The Legend of Zelda "all items" in 31:52.07
Since this category only has RTA records, many references have been made to their runs published on speedrun.com. However, the rules have several differences between RTA and TAS. First, RTA doesn't collect maps and compasses for dungeons. The map at level 1 is located across the water, so in this TAS you don't have to visit it early unless you first get the ladder. And RTA doesn't purchase the potion.
About the Branch Name
A run that completes all items in The Legend of Zelda is named "all items" on this site. However, I'd suggest that, according to some audience's opinions and this judge notes (#6154: fmp & Yuzuhara_3's SNES The Legend of Zelda: A Link to the Past (Japan) "full inventory" in 52:52.44), the branch name might be more appropriate with "full inventory". I don't know much about ALttP, but maximizing inventory upgrades is what both categories have in common, and they both have the same goal. Therefore, I think it is reasonable that this run should also be named "full inventory".
Item Generation
It's not random what items enemies drop. Every items dropping is subordinate to certain rules and patterns. There are 3 memory addresses involved in this.
0x052A: This is responsible for general item drop. The value increases by 1 per enemy when enemy death animation ends. There are baddies whose value increases even if you kill them belonging to group X. Here is a chart Baxter has made in the past.
0x0050: It's called as 10 kill counter. The value increases by 1 for each enemy when an enemy dies. The value is reset to 0 when Link takes damage or reaches to 10. If the 10th enemy is an enemy in group X, it is carried over to the next enemy. Also, this overrides $52A.
If the 10th enemy dies with the bomb, it will drop the bomb.
If Dodongo dies with the sword, it will drop the bomb. Only the first one will be applied if two or more die at the same time, and $52A applies to the rest.
In all other cases, the enemy will drop the blue rupee.
0x0627: It's called as fairy counter. It is reset to 0 only when Link takes damage, and the value increases by 1 per enemy. If the value is 16, enemies will drop fairy and reset the value of $50 to 0. Every time the value is a multiple of 16 doesn't mean the enemy will drop the fairy. Also this overrides $50.
Level Comments
Level 2
The first dungeon that Link could complete without any assets was level 2. Clone statues and blue Leever have been killed for better item drop later. You can obtain the magical key immediately after completing level 2, so we only need to pick up 7 keys in total. Five of them are obtained here. Attacking Gleeok's separated head can manipulate the 10 kill counter. Damaging them with any weapon increases the value by 1 for each frame they take damage. You can easily get a bomb or blue rupee from him (difficult but can also be a fairy) by abusing it.
Level 6 & to Level 8
We don't have bows and arrows yet so just get the ladder and leave. The upcoming level 8 and 4 both have bomb upgrades, and level 4 will cost you 50 rupees additionally, so we still need a lot of money. Buy baits, arrows and win multiple gambles to cover 255 rupees.
Level 8
Reset the game twice because the map, compass, items, and Triforce rooms are far apart from each other. If you give Red Goriya the bait and reset the game, the bait will not be disappeared in your inventory and the path will open normally. This means that for purposes of this category where you need to complete the game with keeping the bait, you can save 100 rupees for time saving. However, this strategy has the risk of having to go back through the previous rooms again after resetting the game, but considering the future route, I decided that it would be better to save the bait.
Level 4
There are many rooms where Gibdos, Darknuts, and Dodongos appear, so it is better to avoid using magical rods or arrows and carry swords and bombs. This category aims to complete the game with all items in hand, so you pay rupees instead of life.
Level 5
Before encountering Gleeok, use all the bombs and swap with the magical rod. Earlier we got the magical book at level 4, which has the side effect of setting the projectile on fire when it hits the target. The magical rod itself does twice as much damage as the wooden sword. So there are cases where it's better to defeat some enemies with the magical rod.
Level 6
Complete level 5 and arrive at level 6 using recorder warping (or Roocoder, named after the discoverer). An awkward explanation of this glitch is described in my previous submission notes. #7512: chatterbox's NES The Legend of Zelda "2nd quest" in 24:48.75
Level 3
Feed the saved bait to the red Goriya. You can prevent the bait from being consumed in the same way as in level 8, but I gave up it because I thought it would be better to buy the shield and bait together from the shop near level 3.
Level 7
Since we got the magical boomerang, it will be replaced with the boomerang instead of a magical rod if all the bombs are run out. You'll have to go through the inventory and equip it with the magical rod, but the level 7 Gleeok has 4 heads, so it's still work as a big time saver.
Level 1
There are two choices for how to complete level 1: 1. Triforce first, compass and map last 2. Compass and map first, Triforce last
Defeating the boss first is meaningful to avoid level ending delays by keeping full-life, however, delays in re-entering the level cannot be excluded from consideration. As a result, the latter was faster.
The last items we have left are letter and potions. The short 50 rupees can be covered by gambling, so resetting the game and using the recorder glitch to reach level 9 is about 200 frames faster than walking from level 1.
Level 9
Lanmolas' (centipede-like enemies) damage-taking routine is similar to that of Moldorms (fire snakes). All segments get invulnerability time when the head takes damage, so avoiding the head and attacking it last can quickly defeat it.
4 fairies were dropped by the fairy counter from Zols killed when picking up a compass. It was expected that the Patra fight would be faster with utilzing beam-sword, but unfortunately this was about 10 frames slower than giving up the fairies.
So far I've made 3 submissions, but still have a lot to learn about this game. A huge thanks to all the Zelda run contributors.