Before jailbreaking, back up your iPad 4 to iCloud or iTunes. If you brick the device (rare, but possible with bad tweaks), you will need to put the device into DFU Mode and restore to 10.3.4—Apple still signs it for the iPad 4 specifically.
So, what are your actual options? There is no "one-click" app like Taurine for this device. You have two viable tools: Phoenix (Nonce) / HomeDepot for 32-bit devices, and the legacy EtasonJB . However, for 10.3.4 specifically, the community has settled on kok3shi or Socket (semi-tethered) . ipad 4 jailbreak 10.3.4
Furthermore, iOS 10.3.4 on the iPad 4 is a or semi-tethered nightmare for most tools. The 32-bit architecture (A6X chip) means you cannot use modern 64-bit jailbreaks like unc0ver or Checkra1n (Checkra1n requires a USB-A to Lightning connection via a hardware exploit, but it maxes out at iOS 14 for phones; for the iPad 4, support is technically there, but checkr1n is tricky on A6X). Before jailbreaking, back up your iPad 4 to iCloud or iTunes
Good luck, and enjoy your vintage tablet! Disclaimer: Jailbreaking voids your warranty and can expose your device to security risks. This guide is for educational purposes. Ensure you comply with your local laws before modifying your device. There is no "one-click" app like Taurine for this device