Good Riddance can only be pursued by unlocking Hardmode which is gotten by reaching Loop 2. Hardmode significantly increases the difficulty of the game which makes Good Riddance one of the most difficult achievements to obtain. Because of this, some players opt to cheese the achievement while others choose to reduce the RNG aspects. This guide will cover the most popular strategies.

As for actually unlocking the weapons, Golden Nuke Launcher (gnuke) is an extremely powerful unlock but is more often than not overkill and may need a decent early secondary to offset this. Golden Disc Gun (gdisc) is more of a meme weapon to unlock but is worth trying out for its obscurity alone. Only one of these weapons are needed to get the achievement and can be done by any character.

Spawning Conditions

Both gnuke and gdisc alike are added to the drop pool starting from 7-2 H1 forwards. Runs are started from 1-1 H1, which is similar to starting on loop.

At the point that 7-2 H1 is reached there is roughly a ~2.56% chance of finding either weapon from the current drop pool at that point, while a full drop pool reduces it to a ~1.85% chance for either. As with any other weapon they all have equal chances of appearing.

On u99r1 only there is a bug present that REQUIRES Crown of Guns in order to get either weapon to drop. This is due to the 'Gun Gun' condition of spawning accidentally being applied on top of the hardmode condition. This is fixed on the Steam betas, where achievements can still be unlocked on. For this reason it's strongly recommended to play on the Steam betas.

There are three main methods in which gnuke or gdisc can be obtained:

Surviving Hardmode

The intended way to unlock Good Riddance is by reaching 7-2 H1 and continue onwards until the desired weapon drop is found. This section will focus on surviving hardmode, which can be helpful to any of the sections.

Hardmode is very off putting to anyone pursuing the achievement because the Desert and Sewers are by far the hardest areas, giving the impression that the difficulty will continue that way. However as the player levels up and better weapons are added to the drop pool, the game becomes progressively more comparable to normal loop gameplay.

The most difficult issues presented by early Hardmode is being swarmed with enemies while running subpar weapons. Elite I.D.P.D. can spawn right away(albeit no vans until H2), two Big Bandits spawn in H1, as well as Mom appearing in the H1 Sewers. Flies are especially annoying being tanky enemies, trying to run into the player's spawn and not having ammo/HP drops. Stack all of these together and the first 4 levels of the game are both unforgiving and extremely annoying, but there are a few ways to mitigate this difficulty.

The best strategy is to run Crown of Death paired with the Golden Grenade Launcher. The extra coverage will help with enemies grouped together to dispose of them quicker, but the extra damage gotten in is significant when considering the elites/bosses. This makes GGL, or for that matter a normal Grenade Launcher, considerably amazing picks for starting a run. This can also be applied on 1-3 H1 to create extra space to deal with Big Bandit spawns, who usually appear early into the level and put incredible pressure on the player. These benefits far outweigh the con of missing out on 1 max HP, though the player should consider taking a weapon that can deal with crowd control in close proximity to avoid blowing themselves up.

If this strategy is not appealing because of the risk of self explosions, then there are other notable options. Golden Assault Rifle is still a viable starting weapon and is a solid pick, though ammunition can be troublesome with a high volume of flies.
Golden Wrench is a decent option as it can deal with the lack of ammunition drops and can handle the spammy amount of maggots and bullets being pelted at the player. The biggest drawback is that Golden Wrench struggles to handle Elites, so a secondary weapon must be depended upon to not risk dying.
There's quite a few crowns to consider, CoProtection may be tempting for the extra health but the extra ammunition can often make or break a run if not depending on melee. CoCurses is always a safe crown to default to over Bare Head, as cursed weapons can come in clutch if finding a higher tier sooner where the earlier areas are particularly difficult. Just be sure to uncurse on 3-2 H1 to avoid the wrath of Cursed Caves.
As for characters, Y.V. is the best for his own strategy listed below, otherwise any character the player is familiar with should be suitable.

Upon getting to Scrapyards the difficulty of the game starts to curve down. There are still spikes in difficulty depending on weapons and mutations, though generally these levels are much easier to handle than early hardmode. From this point the player should focus on hitting ultra and finding good weapons to survive with. All 3 vaults should be visited as well as Pizza Sewers in H1, as these will increase difficulty making it so gnuke/gdisc can drop starting from multiple areas earlier. The biggest factors of each run is getting past the first few areas, getting good weapon rng and being able to actually find the drops. This achievement grind is a matter of persistence more than anything. Upon finding either gnuke or gdisc, either can be picked up and the level can be exited thus unlocking the weapon and Good Riddance.

The Y.V. Strategy

Y.V. plays fairly similar to trying to achieve Good Riddance normally, though he speeds up the process and can reduce the rng/risk factors by quite a bit. In terms of risk:reward this guide is the most recommended, as Y.V. is a very strong character to start hardmode with because of his active and passive, but also takes the best shortcut to getting the weapon that gives pretty good chances to get the achievement on the first successful run.

Hardmode should be gone about as the player normally would, but be playing as Y.V. specifically. The goal is to hit Ultra on 4-1 H1, though doing it in the Frozen City/later is also acceptable. Upon reaching Ultra, Y.V. can take either Ima Gun God or Back 2 Bizniz, as the important part is being able to access Y.V.'s Crib. Entering the secret area will give Y.V. two giant weapon chests which contain 25 weapons each, and gnuke/gdisc exists within that drop pool. If found the player can simply exit the level with it, unlocking the weapon as well as Good Riddance.

The reason that Ultra should be hit on 4-1 H1 is because Crib specifically gives difficulty from up to 6 areas above, which exactly lands on 7-2 H1. Secret areas should be skipped to not increase difficulty and give the optimal odds, though the % chance isn't that significant it's still smart to give oneself the best statistical odds. Do not take unnecessary risk to get every single rad that drops, Sewers and Caves are especially good areas for quick level ups and hitting Ultra should come natural without having to constantly put oneself in harm's way.

Any mutation/crown for survival is fine, however one that stands out is Open Mind, which SHOULD be taken. Open Mind gives a 3rd giant weapon chest in Crib, which increases the number of weapons seen from 50 to 75, which significantly increases the chances of seeing a desired golden weapon. The only thing that needs to be avoided is Crown of Love, as the giant weapon chests will convert to giant ammo chests making this entire strategy guide useless.

As for u99r1, Y.V. can run CoGuns with Golden Wrench to mitigate the downside of no ammo drops. His extra firing rate comes in handy, and with long arms he will be able to chip away at tanky enemy health while mostly being able to avoid taking damage because of how quickly he is able to swing gwrench. Melee runs will always go a lot slower, but by no means makes this option unviable.

The Gun Gun Strategy

The final strategy will minimize the time spent playing Hardmode but has the potential to be the most grindy/annoying. If done right it will guarantee the weapon will appear eventually, patience is the name of the game. The general idea is to get Gun Gun into the proto chest from a normal run, then visit the first vault in Hardmode and continually get energy drops from a Crown Guardian's attacks to shoot Gun Gun extra times until gnuke/gdisc spawns.

Step one is to get the Gun Gun into the proto chest. Start a normal run as any character (NOT Hardmode) and get to loop using Crown of Guns. From 1-2 L1 forward a unique weapon called 'Gun Gun' will appear if the aforementioned conditions are met. Until Gun Gun drops do NOT visit all 3 vaults, just visiting 1 or 2 will be sufficient. Upon reaching Gun Gun, reach the next vault and put the weapon into the proto chest, exiting the level. From here the level will be stored and can be accessible again via proto chest, whether in normal or Hardmode.

Step two is now to start a normal run on Hardmode with the Golden Wrench and reach the H1 1-2 Vault. Any character works, however Robot is the most optimal choice. A crown MUST be started with to see the proto chest, the most optimal here is to take CoRisk to boost ammo drops while at full HP. If playing risk averse then CoHaste is a suitable replacement, however less optimal. Leveling up once or twice is most likely by the vault, but these mutations can have a significant impact on the easiness of the grind. Rabbit Paw and Long Arms are extremely useful to ease up the process. Following these other decent picks are Stress, Strong Spirit and Rhino Skin for the sake of safety reasons.

Step three in the vault is to collect the Gun Gun from the Proto Chest, as the player should now be running Golden Wrench and Gun Gun. Two statues that spawn Crown Guardians will spawn here, breaking one will activate the other just as standing on the crown pedestal will activate both. From here ONLY kill one Crown Guardian, thea other needs to be kept alive on purpose.

Gun Gun costs 40 energy ammo to shoot and will give 1 random weapon from 10 areas or above*. This makes the weapon pool stretch far enough that gnuke/gdisc can be included in the drop pool while in the 1-2 H1 Crown Vault.

Shooting Gun Gun does damage to enemies, so it is possible to kill the Crown Guardian this way. The player should be especially careful to avoid this, but if done then Gun Gun can be returned to the Proto Chest if possible and simply just return to vault again on a new run.

From here the process is simple. At 40 energy or above shoot Gun Gun. If not the desired weapon, then use the Golden Wrench to break orbs shot by the Crown Guardian to build ammo back up. They will only fire when within line of sight, so hiding behind walls the entire time will not work. The large orbs shot by the Crown Guardian can one-shot Robot with or without Rhino Skin so extra caution should be applied, always be standing about a screen's width/height from the Guardian to minimize risk.

Robot can eat weapons dropped by Gun Gun, it should be done that the eaten weapon is in the primary slot and Gun Gun in the secondary to maximize the chances of getting energy. However only do this outside of the line of sight of the Crown Guardian, as a fast traveling orb can result in death or a misinput eating the Golden Wrench/Gun Gun instead.

From here it is all up to luck, as it is possible to get gnuke/gdisc on the very first shot or it could take a hundred times. Once it is gotten, simply complete the level with the golden weapon in hand to obtain Good Riddance.

As for u99r1, this strategy still works but is just less effective. The setup has to be Robot with CoGuns and a melee(Golden Wrench). The giant orbs will no longer drop ammo but will instead drop weapons which Robot can eat. Rabbit Paw is no longer useful here, Long Arms should be prioritized followed by Stress/Spirit for safety.

* At first glance at the hardmode drop table (link later) gnuke/gdisc are 12 areas ahead where gun gun only pulls from up to 10, this still works as any character due to (link explanation)