I would advise against it but if things get messed up you should be able to fix it by booting an old kernel and removing this one. Something like this ...



Boot from CD

mount -o bind /dev  /dev

mount -o bind /proc  /proc

chroot 

apt-get install 

update-grub

From comment by Tomas an easier method:

By entering GRUB through holding shift during boot you can enter the "Previous versions" of Linux. There you can select your old kernel, which is by default not removed.

Now if you still want it ...

Download the three .DEB files with the name starting with linux from here: http://kernel.ubuntu.com/~kernel-ppa/mainline/v3.4-precise/

Example for i386 (take the 2 with amd64 in the name for 64-bit and pae in the name for i386 with 4+Gb memory; check uname -a if you are unsure!):

linux-headers-3.4.0-030400_3.4.0-030400.201205210521_all.deb

linux-image-3.4.0-030400-generic_3.4.0-030400.201205210521_i386.deb

linux-headers-3.4.0-030400-generic_3.4.0-030400.201205210521_i386.deb

Install all 3 packages ...

Example for i386

sudo dpkg -i linux-headers-3.4.0-030400_3.4.0-030400.201205210521_all.deb    

sudo dpkg -i linux-headers-3.4.0-030400-generic_3.4.0-030400.201205210521_i386.deb

sudo dpkg -i linux-image-3.4.0-030400-generic_3.4.0-030400.201205210521_i386.deb

Reboot your system ...

sudo reboot

Test it ...

uname -r

This should show a kernel with 3.4 in the name.

Now for the good news ...

"This release includes several Btrfs updates: metadata blocks bigger than 4KB,

much better metadata performance,

better error handling and

better recovery tools.

a new X32 ABI which allows to run in 64 bit mode with 32 bit pointers;

several updates to the GPU drivers: early modesetting of Nvidia Geforce 600 'Kepler', support of AMD RadeonHD 7xxx and AMD Trinity APU series, and support of Intel Medfield graphics;

support of x86 cpu driver autoprobing, a device-mapper target that stores cryptographic hashes of blocks to check for intrusions, another target to use external read-only devices as origin source of a thin provisioned LVM volume,

several perf improvements such as GTK2 report GUI and

a new 'Yama' security module."

You can help test official 3.4 support in 12.04 by following these instructions: http://www.theorangenotebook.com/2012/06/call-for-testing-1210-kernel-on-1204.html