This achievement will take a bit of playtime to unlock, the life of a street performer isn't glamorous folks
IF YOU HAVE NOT ALREADY STARTED YOUR PLAYTHROUGH I HIGHLY SUGGEST YOU PICK A BARD
While it is possible to unlock musical instrument proficiency on other characters, bards will start with it meaning as soon as you begin your adventure you can take to the streets to begin performing/begging
To perform open your action menu and select your instrument of choice and song to begin playing, once the performance has started nearby NPCs will crowd around and (if your lucky) each crowd member may bless you with the ocasssional single gold piece. Single. As in one. Yeah.
Your options are to either perform until your fingers bleed in the biggest population center you find until you get all 100 required, or if progressing through the game normally to avoid a bit of grind you can just perform for a while each time you encounter new groups of people. Below I'll list areas populated with NPCs ready and willing to throw pity change at you, Good Luck!
Act I
Tiefling Refuge at Emerald Grove (main location of Act 1, can't miss it)
Druid's Grove (inside Emerald Grove past Tiefling Refuge Camp)
Waukeen's Rest (northwest of Emerald Grove, help the people there get their friend out of the building on fire before playing some fire beats)
Goblin Camp (western area of the map, south of Waukeen's Rest)
Githyanki Creche (after entering the Mountain Pass area, they can be found inside the temple)
Grymforge (area in the Underdark reached via boat ride at the Decrepit Village)
Act II
Last Light Inn (central area of Act 2, progress through the Shadowlands until scene where Harpers will lead you to the area for shelter, easier to find if entering from Underdark)
Moonrise Towers (southern most point in the Shadowlands area, you will be going here eventually as the plot revolves heavily around this location)
Act III
Baldur's Gate
If you have progressed to Act 3 and have still not accumulated your 100 gold from performing, you will be doing your remaining performances in the titular city Baldur's Gate, the largest and most populous city available to you
Additional Tips
Sometimes you get gold, sometimes you get no gold, sometimes you might get gold but it doesn't count toward your progress. If you keep an eye on your progress and get gold from performing and notice the progress from 0-100 has gone up I recommend you save to be safe. In the event you find you're obtaining lots of gold but getting no progress, try loading save files and keep an eye on progress until it starts going up again