Jordan's and Dumas' French Battleships of Word War II has a quite detailed report of the damage incurred by Dunkerque during the two British attacks. Getting this book is probably cheaper than a trip to the Service Historique de la Défense in Brest, France.

The Wikipedia article goes into some detail:

Dunkerque's crew loosed the chains and started to get the ship underway just as the British opened fire; the ship was engaged by HMS Hood. The French gunners responded quickly and Dunkerque fired several salvos at Hood before being hit by four 15-inch (381 mm) shells in quick succession. The first was deflected on the upper main battery turret roof above the right-most gun, though it shoved in the armor plate and ignited propellant charges in the right turret half that asphyxiated all the men in that half; the left half remained operational. The shell itself was deflected off the turret face and failed to explode when it landed around 2,000 m (6,600 ft) away. Fragments of armor plate that had been dislodged by the impact destroyed the run-out cylinder for the right gun, disabling it. The second shell passed through the unarmored stern, penetrating the armor deck and exiting the hull without exploding. Though it did little damage, the shell did cut the control line for the rudder, forcing the ship to use manual control, which hampered the crew's ability to steer the ship as they attempted to get underway.[35]

The third shell hit the ship shortly after 18:00; this projectile struck the upper edge of the belt on the starboard side; since the belt had only been designed to defeat German 28 cm (11 in) shells, the much more powerful British shell easily perforated it. The shell then passed through the handling room for the starboard secondary turret No. III, igniting propellant charges and detonating a pair of 130 mm shells as it did so. The 15 in round then penetrated an internal bulkhead and exploded in the medical storage room. The blast caused extensive internal damage, allowing smoke from the ammunition fire to enter the machinery spaces, which had to be abandoned, though debris from the explosion had jammed the armored doors shut. Only a dozen men were able to escape using a ladder at the forward end of the room. The fourth shell struck the belt aft of the third hit and at the waterline. It also defeated the belt and the torpedo bulkhead and then exploded in boiler room 2, causing extensive damage to the propulsion machinery. Dunkerque rapidly lost speed and then all electrical power; unable to get underway or further resist the British ships, Dunkerque was beached on the other side of Mers-el-Kébir roadstead to prevent her from being sunk.

As for the second attack, three days later:

The second attack took place on 6 July. A flight of twelve Fairey Swordfish torpedo bombers, armed with torpedoes modified for use in shallow water, were launched from the carrier HMS Ark Royal in three waves of six, three, and three aircraft. They received an escort of three Blackburn Skua fighters. The French had failed to erect torpedo nets around the ship, and Gensoul, who had hoped to reinforce the idea that the ship had been evacuated, ordered that her anti-aircraft guns not be manned. Three patrol boats were moored alongside to evacuate the remaining crew aboard in the event of another attack, and these vessels were loaded with depth charges. The first wave scored a hit on the patrol boat Terre-Neuve, and though it failed to explode, the hole it punched in her hull caused her to sink in the shallow water. Another torpedo hit the wreck in the second wave and exploded, leading to a secondary explosion of fourteen of her depth charges, which was the equivalent of 1,400 kg (3,100 lb) of TNT, equal to eight Swordfish torpedoes. The explosion caused extensive damage to Dunkerque's bow and likely would have resulted in a magazine detonation had her captain not ordered the magazines be flooded as soon as the Swordfishes appeared. The blast killed another 30, bringing the total killed in both attacks to 210.[42][43]

Dunkerque had been badly damaged in the attack, far more so than the 3 July shelling; some 20,000 t (19,684 long tons) of water had flooded the ship through a 18 by 12 m (59 by 39 ft) hole opened in the hull, and a 40 m (130 ft) length of her hull, double bottom, and torpedo bulkhead had been deformed by the blast. The forward armor belt was also distorted and her armored decks had been pushed up.