Exalted Companion allows the Druid to have a Celestial Creature animal companion, which has Int to 3 if it was lower, and a good alignment. However, it does not retroactively update their current companion to a Celestial creature. They would need to dismiss their current companion and summon a new one with the template, it's an inherited template so a creature must be born with it. Granted you (as DM) could hand wave the part about replacing the current companion, and just have her perform the ritual as though summoning a new one to modify her existing companion. In either case the new version of the companion would have all the default feats and skill ranks of a MM Tiger, and she can repick those for any additional HD from being an animal companion.

Vassal of Bahamut requires Craft (armorsmithing) 5 ranks and Diplomacy 5 ranks, with Int 3 it only gets one skill point per HD, and those are cross-class skills for it. It can't reasonably expect to take ranks in either skill without Int 3+, but on top of that you can't reasonably expect a tiger to be able to learn to craft armor, and Celestial Creature doesn't grant any languages so you also can't reasonably expect it to learn diplomacy. Even if it could learn those skills, gaining ten cross-class skill ranks takes twenty skill points, at one skill point per HD it couldn't hope to qualify until it has 26 HD.

Animal companions don't gain experience points, if it doesn't gain experience it can't gain class levels. Even if it did, you would need to assign a LA for the tiger itself, it would have another +2 LA for Celestial Creature, and all of its HD including those from being an animal companion count toward its ECL. It would start at 0 xp and need to gain a portion of the party's xp if it ever hopes to level up.