Installing a Boot Animation without using Root Explorer
ES can read/write to protected folders, you just have to enable it in your settings. Open the settings menu (press the menu button, then select "Settings") and find the "Root Settings" item, then enable "Root Explorer" (operate with root permission) and "Mount File System" (allow writing to /system).

Alternatively, many devices/Android versions should allow you to simply put the bootanimation.zip file into /data/local instead of /system/media. You won't need a root explorer for this since /data/local is world writable. This doesn't work on all ROMs, though.

Screenshots for the ES settings: