The achievements Golden cookie, Lucky cookie, A stroke of luck, Fortune, Leprechaun and Black cat's paw are achievements acquired by clicking 1, 7, 27, 77, 777 and 7777 Golden Cookies respectively. Golden Cookie clicks remain in all subsequent playthroughs so you can soft reset. Early bird and Fading luck are achievements acquired by clicking a Golden Cookie less than 1 second after it appears and before it fades, respectively. None of these achievements have flavor text, except for Fortune, which says "You should really go to bed.".
For the purpose of counting "Golden Cookies", both Golden Cookies and Wrath Cookies are fair game.
Getting these achievements takes a relatively long amount of time, as Golden Cookies are rare to start with. However, the game saves your total amount of clicks, so it is safe to ascend, and acquire these achievements in several sittings.
The more Golden Cookies the player gets, the easier the subsequent achievements become, as the unlocked upgrades Lucky day (7 Golden Cookies) and Serendipity (27 Golden Cookies) will each double the appearance rate and staying duration of Golden Cookies.
Even then, Golden Cookies remain a relatively rare occurrence (the right upgrades will allow one to spawn approximately every 2 minutes). A good strategy to get many Golden Cookies quickly is to try to activate Cookie Chains, as each cookie in the chain will be counted. For this, it is preferable to activate the Grandmapocalypse, as Wrath Cookies have roughly 6% chance to trigger a cookie chain, which is 20 times higher than Golden Cookies. Depending on the player's skill, bank, and luck, each chain should give a rough 10 to 15 cookies.
Version v.2.002 introduces both Early bird and Fading luck, while also making Golden Cookies spawn at a very small size with an equally small clickable bounding box, with both cookie and box growing and pulsing as they fade in, making them very difficult to spot within one second. However, both achievements can be acquired by clicking Golden Cookies during a Cookie Chain, where they appear and grow much faster than normal, so this is probably the best time to try for Early bird. Another (luck-based) strategy for getting Early bird is to be clicking the Big Cookie during the time the next Golden Cookie is expected to spawn; if by chance it spawns in where the player is already clicking, it can be clicked before it even becomes visible to the player (this is made more difficult than before by the smaller-to-start bounding box, but is still possible).