Maximum Pressure of Covalently Bonded Material
With the twist of thumbscrew, a hand-held diamond anvil cell will exert 300 GPa (43,500,000 psi).  No chemical bonding problem there. If you stack stuff - planetary and stellar cores - it gets more interesting, depending on composition and temperature.  Temperature matters.  

http://en.wikipedia.org/wiki/Electron_degeneracy_pressure

Magnetic fields exert pressure.  How much magnetic field diddles with chemical bonding to give you a pressure estimate?

http://en.wikipedia.org/wiki/Magnetar 
http://en.wikipedia.org/wiki/Magnetic_pressure 
  10^10 teslas is 4.0×10^25 J/m^3 E/c^2 mass density more than 10^4 times that of lead.  

That'll put some hurt on chemical bonding.  Scale down to 347 kJ/mole-bond multiplied in a molar volume of diamond.  Atomizing diamond requires about 800 kJ/mol per atom against cohesive energy.  The strongest chemical bonding interaction is roughly 3 eV.  Then you can pontificate with a Lennard-Jones potential.

http://en.wikipedia.org/wiki/Lennard-Jones_potential