A safety hint.
If you decide you've just got to look at the AC Mains with a battery powered oscilloscope, reconsider, if you still decide 'I just have to do this...' then consider using a AC mains to 12 to 30V step down transformer. The transformer will isolate you and pass the 50/60Hz. It will show you the turn on of a SCR/Triac light dimmer.
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If you believe you need higher accuracy, reconsider why? What are you looking for? High frequency noise on the AC mains?
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OK you've decided to play Russian Roulette.
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Obtain a 9K 10W resistor, obtain a 1K 10W resistor, wire in series. I like the Dale aluminum body units because you can mount them on a heatsink that you can connect to the safety/protective ground.
Wire one end of the 9k to the AC Mains hot, wire the other end to the 1K, wire the other end of the 1K to neutral.
Monitor the voltage across the 1K, it will be 1/10 the incoming voltage.
Touching it and ground probably won't hurt or kill you. Just tested mine while sitting on a chair in a 1/4" sheet of Lexan. Used my right finger and thumb. As expected I felt nothing. This is still stupid silly but the safest way to actually directly monitor the AC mains.
However, I doubt your scope will see any HF trash on the AC mains.
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I live to fight EMI/RFI, interference on the AC Mains created by all the switch mode power supplies.
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I have an intrinsically safe AC Mains to communication receiver, spectrum analyzer interface that has been hi-pot tested over night with 10kV on the AC mains side.
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In addition to extreme isolation from the AC Mains voltage, either 120V US, 240V the rest of the world, the output is clamped at +/- 2.1V.
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It was an extremely non trivial project, the actual schematic is bog simple, obtaining components that could withstand 10kV for ~10 hours was the royal PITA.
Capacitors large enough to pass 50kHz with "no loss" and withstand 10kV are rare. And pricey.
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There are commercial units
https://www.reliantemc.com/laplace-voltage-probe-plip/
https://www.onfilter.com/test-and-measurements
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These are serious scientific instruments not "magic hocus pocus dirty power will harm your health or kill you."
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If you can't afford either, and if you don't have the skill set and access to a certified hi-pot tester, to roll your own, don't.
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Again, before monitoring the AC Mains for anything but voltage with a meter and current with a clamp on, really think "Do I need to do this?"
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With "Why do I need to look at the AC Mains."
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Death is for keeps.
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[The afterlife doesn't count because we won't be bothering with such trivial things in heaven or hell of Valhalla or 贵ó濒办惫补苍驳谤. <sorry for the font change there, had to look it up> I'd cover more religions but can't think of their afterlife policies off the top of my head right now, but I'm pretty sure none of them suggest we'll much care about earthly problems.]?
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I lost a friend in college who was trying to look at the AC Mains with a scope and isolation transformer. He was alone so I don't know how he screwed up. Smart guy, not prone to foolishness, yet he died.
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So yea I'm a bit too focused on the safety issues with scopes and AC Mains.
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Going to the funeral for a good friend sucked bilge water.
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