From left to right:

Causal nexus achievement: 5 or more chain collapses in a row
Skilled traveler: visited every city along the silk road
Adventure campaign achievement: adventure campaign completed
River crossing achievement: beat all adventure campaign crossing the Nile levels
Riddle of the Sphinx achievement: puzzle campaign completed
Human net achievement: caught all drops in a level
Coin collector achievement: over 1000 Ankh coin collected
Power-ups achievement: upgrade all power-ups to maximum
Revealer of secrets achievement: all bonus levels unlocked
Eliminator achievement: more than 10 matches in a row
Defender achievement: beat all adventure campaign onslaught levels
Sharpshooter achievement: 100% accuracy on one level achieved

Below is the route map:



You can explore the map freely but it's highly recommended to obtain the chariot first, which allows you to fast travel to any city you have already visited. The chariot pieces are shattered in the northeast area, so you can go like Tyre -> Babylon -> Rey -> Merv -> Samarkand -> Kashgar etc. until you obtain all pieces. Levels will get harder when you visit more cities, so it's important to assemble the chariot as soon as possible before levels become harder.

Then you can visit all the cities, find all artifacts, and unlock all bonus stages with the help of chariot.

Next, to unlock the onslaught and river crossing achievements, you'll need to visit most of the paths. Using the route map above, you can check the route you have visited so that you don't travel on a same route twice. Unvisited routes will be marked red, or you can travel to Luxor and see which routes are already visited.

Then you can farm coins to buy everything in the store and then finish the adventure campaign.

Only 21 levels, which is half of Luxor 3, and also easier than Luxor 3. Most levels are straightforward and only two levels need to be mentioned:

Causal nexus: Easily missable, but this one has been through the entire Luxor series. Just create a x5 chain string manually in early game and trigger it (e.g. GGRRRYBBGGBYYRGGG and shoot the green in bold).
Human net: Could be hard if you are not good at catching. Upgrade net to maximum and hit green on the third match, or wait for the ball strings to go closer to the pyramid so that the scarab bursts into fewer jewels when the string is destroyed.
Eliminator: Easily done in early game since the ball string are easier. Or wait until turquoise is added in normal difficulty, then utilize the color sort power-up (hail to the greatest Egyptian god, Thoth).
Sharpshooter: Has been through the entire Luxor series as well. Be patient and accurate.