Throughout the game there are several women that you can potentially date. Once you take them out, if they like you enough you bring them back home and you will have the option to take them to bed, which nets you the achievement/trophy. How much they like you is based on several factors, such as the car you're driving, where you purchased your clothes, and where you take her.
The earliest and possibly easiest way to do this is with Michelle after the mission "Three's a Crowd." The first date with Michelle is actually the mission, so all you have to do is pick a good car, clothes, and venue. Michelle actually likes Niko's russian clothes already and also likes darts and pool the most, which are both close to her house. She also already likes Roman's cab too, although it appears her favorite car is the Merit. After you date her the first time, wait a few days and try calling her, if that doesn't work wait some more time and try again to get a second date. She will also eventually call you for a second date. If she calls you dont decline the call or to see her as this will decrease your "friendship" level and the chance of you getting lucky. Also remember to change to different clothes from your first date and to drive carefully as these both influence your "friendship" level as well. Once you complete the second date if she likes you enough you will get the option to "try your luck" once you drive back to her house and are still in the car. A short cutscene will play and you will re-appear back outside her house and the achievement/trophy will pop.
Listed below are the women possible to date, how to meet them, the cars they most prefer to be picked up in, their favorite clothing stores, their top four or so favorite social venues (% is based on how much the woman likes that place, out of 100), and finally if sleeping with the woman nets you any special ability. If you sleep with one of the women that do have an ability, there is no rhyme or reason to when they offer it to you. Sometime after you sleep with them you will receive a call from the woman offering her services.
**This can be done after completing story mode**
***Also if you have the Ballad of Gay Tony expansion the achievement is slightly easier as you can simply dance with a girl in a club and then call her and visit for a "booty call" afterwards, which also unlocks the achievement/trophy.***
Name: Michelle
Acquired: Complete "Three's a Crowd"
Favorite Cars: Roman's Cab, Merit, Voodoo, Banshee, Blista
Favorite Clothiers: Russian, Hats, Glasses
Favorite Venues: Darts (80%), Pool (80%), Comedy (75%), Steinway Beer Gardens (70%), Lucky Winkles (70%)
Name: Carmen Ortiz
Acquired: Date "SoBoHoe" from Love-meet.net after completing "Out of the Closet"
Favorite Cars: Sultan RS, Dukes, Stallion, FXT, E109
Favorite Clothiers: Modo, Perseus
Favorite Venues: Any Drinking/Club (90%), Darts (80%), Strip Club (80%), Cabaret/Comedy (80%)
Special Ability: Can heal you when you're injured by calling her
Name: Kiki Jenkins
Acquired: Date "LawChick" from Love-meet.net after completing "Out of the Closet," and unlocking the island of Algonquin
Favorite Cars: Washington, Chavos, Dilettante, Marbella, Willard
Favorite Clothiers: Russian, Hats, Glasses
Favorite Venues: Jerkov's (85%), Club Liberty (85%), Pool/Dart/Bowling (80%), Cabaret/Comedy (80%)
Special Ability: Can get rid of up to a 3 star wanted level by calling her
Name: Alexandra Chilton
Acquired: Date "Liberated Woman" from Craplist.net after completing "Out of the Closet," and unlocking the island of Algonquin
Favorite Cars: Huntly, Turismo, Stretch, Infernus, Cognoscenti
Favorite Clothiers: Perseus
Favorite Venues: Pool/Dart/Bowling/Strip Club (80%), Cabaret/Comedy (80%), Steinway Beer Gardens (70%), Lucky Winkles (70%)
Special Ability: You will get all clothes in the city for half price for 24 in-game hours after she offers it to you
Name: Kate McReary
Acquired: Complete "Waste Not Want Knots"
Favorite Cars: Rebla, Patriot, Comet, Habanero, Super GT
Favorite Clothiers: Russian
Favorite Venues: Darts (80%), Pool (80%), Steinway Beer Gardens (70%), Lucky Winkles (70%)