Here is the full list of all 32 Spelunky 2 achievements.
Reach the Black Market in a non-seeded run.
Unlock the entrance.
Complete 50% of the Journal or more.
Obtain the Kapala in a non-seeded run.
Complete the Moon Challenge in a non-seeded run.
Reach the Ice Caves in a non-seeded run.
Make it past Olmec's Lair in a non-seeded run.
Obtain some royal headwear in a non-seeded run.
Make it past 1-4 in a non-seeded run.
Obtain all other achievements.
Complete the game in a non-seeded run.
Complete the game without using shortcuts in a non-seeded, single-player run.
Complete the game in 10 minutes or less without shortcuts in a non-seeded, single-player run.
Complete the game with no gold without shortcuts in a non-seeded, single-player run.
Reach the Sunken City in a non-seeded, single-player run.
Complete the game by defeating Hundun in a non-seeded, single-player run.
Reach the Cosmic Ocean in a non-seeded, single-player run.
Complete the Star Challenge in a non-seeded run.
Complete the Sun Challenge in a non-seeded run.
End a run with $1,000,000 or more in a non-seeded, single-player run.
Complete the Journal.
Unlock the first shortcut.
Unlock all three shortcuts.
Finish the Tutorial Speedrun in under 30 seconds.
Win a First-to-Five Deathmatch against three bots using the Default ruleset.
Bring two turkeys to Yang in a non-seeded run.
Buy out Yang's Pet Shop in a non-seeded run.
Enter Madame Tusk's Palace of Pleasure as a guest (in a non-seeded run).
Reach the City of Gold in a non-seeded, single-player run.
Obtain the Ankh in a non-seeded run.
Obtain the Tablet of Destiny in a non-seeded run.
Wake the Eggplant Child in a non-seeded run.