Safari uses a different free app called Userscripts. After installing, open Safari → Settings → Extensions and enable it. Then tap "I've installed it" below.
iPhone uses an app called Userscripts (Tampermonkey doesn't exist on iOS). After installing from the App Store, you also need to:
Open iPhone Settings → Safari → Extensions, tap Userscripts, toggle it on, and set Other Websites to Allow.
Come back to Safari, tap the "AA" in the address bar → Manage Extensions, and make sure Userscripts is enabled.
Then tap "I've installed it" below.
Step 2 — Install the Skip Script
Click the button below. Tampermonkey will pop up a dialog showing the script — click Install in that dialog.
Saw a "Script Installation" page from tampermonkey.net?
That page only appears when Tampermonkey isn't installed (or isn't enabled in this browser). Go back to step 1, install it, then come back. If you installed it in a different browser, open this wizard in the same browser as Tampermonkey.
On iPhone: tap Install Skip Script. The Userscripts extension should offer to save the script — tap Save / Allow. If you instead see plain script text in Safari, tap-and-hold → Select All → Copy, open the Userscripts app, tap + → New Userscript, paste, and save. Either way, finish by opening the Userscripts app and confirming the script's toggle is on.
Other troubleshooting
If the script appeared as plain text or downloaded as a file, Tampermonkey isn't picking it up. Confirm the Tampermonkey icon shows in your browser toolbar, refresh this page, and try again.
Step 3 — Try it out
Open Crunchyroll and play any episode. Skip Intro, Skip Credits, and Next Episode buttons should now click themselves.
Verify it loaded: on Crunchyroll, open DevTools console (Cmd+Opt+J in Chrome / Cmd+Opt+C in Safari). You should see [cr-autoskip] active in orange.
Updates
Tampermonkey checks for script updates daily on its own. You'll get a small "update available" badge — click it once and you're current. No need to revisit this page.