Other procedure you could try if my above advice still hasn't helped enough.
First, connect your iPad to USB and sync and backup your iPad to iTunes (make sure your iTunes is up to date).
Then disconnect/eject your iPad from the computer.
From just the iPad, in the Settings App under the General setting, look in the right column for Reset option, then erase and reset your iPad to completely erase your iPad and then, again, from the iPad, set it up as a new iPad setup to factory "out of the box" operation.
Do not set up any Wifi networks AND do not setup any iCloud services.
Then reconnect your iPad to the computer and make sure to cancel the syncing, by tapping the small X to the left in the top center iTunes display box.
iTunes should detect your iPad. If iTunes begins to try and sync, again, cancel the sync.
Setup iPad as new from iTunes.
Once done, THEN, select restore from backup and use the previously created backup to restore your iPad.
Once the restore is complete, finish setting up the iPad and let it sync back to iTunes you can either cancel the sync, again or let it backup, again.
Then disconnect /ejectthe iPad from the iTunes and the computer.
Do one hard reset of your iPad by holding down both the Home and sleep/wake buttons simultaneously until your iPad goes to black and restarts with Apple logo, then release the buttons.
Once your iPad is back to the Home screen,
In the Settings App under the General tab, to the right under Spotlight sesrch, try disabling the search under apps that really do not need a search, like some games, remotes, apps that really do not need to be searched, etc., to reduce the list for Spotlight to search.
Try turning on Reduced Motion.
This is found in the Settings App in the General tab the left panel.
In the right panel look under Accessibility, the look for Reduce Motion and turn this feature "On".
You should see an appreciable performance increase on all iPad 2, 3 and 4 models.
In the Settings App under the General Tab, in the right column, look for Background App Refresh and turn this setting to "off".
Good Luck!