Here, I'll guide you through the most effective approach to advance your entire Atlas in POE 3.23 Solo Self-Found. And here are some most helpful tips that have proven successful for me.

Complete Unique Maps

Progressing and completing the Atlas in SSF can pose challenges, particularly for newer players. However, there are strategies you can leverage to ease the process. As you're aware, the inability to buy maps is a significant obstacle, requiring you to utilize other resources effectively.

Among the most daunting tasks on the Atlas are unique maps, given their rarity compared to normal, magic, or rare maps. Kirac reports and missions for unique maps are also scarce. Hence, before delving into Atlas mechanics, prioritizing the completion of unique maps is advisable. Never overlook a unique map during your initial Atlas exploration.

The sole method ensuring a unique map within your Kirac missions is a Singular Kirac Report, which rerolls all missions to include at least one unique map. However, even with this, there's no guarantee of encountering one you haven't already completed.

Important Atlas/Map Mechanics

But what are the actual important mechanics that you need to know of? There are Natural Tiers, Kirac Scouting Reports, Kirac Missions, Kirac's Trade Inventory, and Orbs of Horizon.

Natural Tiers

Firstly, the Natural Tiers serve as the foundational and original tiers of a map. Each map is initially designated to a specific tier, categorized as white, yellow, or red. These map tiers are subject to enhancement through the utilization of Voidstones. This is where confusion may arise for some individuals.

For instance, one might encounter a Dunes Map labeled as yellow tier 9 due to the presence of 2 Voidstones. However, while this may be accurate, it does not contribute towards fulfilling the Atlas objective. The true and intrinsic tier of Dunes remains white tier 2, crucial for the initial completion of the Atlas objective. Once achieved, this distinction becomes inconsequential. Nonetheless, it's imperative to remain cognizant of this aspect.

Hence, ensure that you have no Voidstones or any other Atlas modifiers equipped.

Kirac Scouting Reports

Regarding Kirac reports, they facilitate the rerolling of Kirac missions, with various types available for different purposes.

Throughout your Atlas progression, the necessity for different reports will vary. Therefore, ensure to collect every report you encounter and reserve them for essential use only. Trust me, they become invaluable when options are scarce.

Ensure that you've fully invested in Kirac missions within the Atlas tree to increase the likelihood of receiving diverse reports more frequently. For instance, if your objective is to complete corrupted red tier maps, utilizing a Vaal Scouting Report simplifies the process by transforming all Kirac missions into corrupted maps whenever feasible. Utilize each scout report strategically as per the situation.

However, specific scouting reports may not always be necessary. For instance, if your primary focus is on obtaining unique maps, employing every available scout report becomes imperative. Pray for a unique map mission since only one report can reroll missions to unique maps, which may not drop frequently.

Kirac Missions

During the process of rerolling Kirac missions, you may encounter another challenge: running out of Kirac missions entirely.

However, there's a tried and tested solution for this as well. You'll want to employ the boss rushing technique and traverse as many maps of the desired tier as necessary.

Upon slaying the boss of a map, you stand a chance to obtain a Kirac mission. This task is simpler in white and yellow tier maps due to weaker bosses. However, if your build is capable of handling tier 16 maps, you'll encounter no issues regardless of the tier.

Ensure once again that you've fully invested in Kirac within the Atlas tree to heighten your chances of receiving Kirac missions upon map completion. Subsequently, embark on a spree of boss rushing for approximately an hour, yielding multiple missions.

Kirac's Trade Inventory

Next, Kirac's Trade Inventory enables you to purchase maps directly from Kirac.

These inventories reset with each completed mission. Therefore, each time you finish a mission, remember to inspect his inventory as you might find an incomplete map available for purchase without expending a Kirac mission.

Orbs Of Horizon

Lastly, I'd like to highlight Orbs of Horizon, often overlooked but potentially valuable in early Atlas progression.

These orbs allow you to swap your current map for another of the same tier. While this method may not always yield incomplete maps reliably, during the initial stages of your Atlas journey, you'll often discover uncompleted maps using them. However, as your Atlas fills up, the likelihood of receiving maps you've already completed increases.

Those were my key tips for advancing through the Atlas in SSF, applicable to players of any skill level. Progressing takes time, so don't be disheartened if you encounter obstacles. If you feel stuck, it's sometimes beneficial to take a break. Whether you're low on missions, reports, or struggling to find specific maps, stepping away momentarily can help. Temporarily set aside the goal of completing the Atlas and engage in other activities. With consistent gameplay, progress will naturally occur. Avoid fixating too narrowly on one approach. Keep experimenting and adapting.