Putting ceramic tile over hardwood floor?

Stripped old vinyl flooring down to the original 1942 hardwood floor in the kitchen. Had the floors repaired and refinished but they ended up looking terrible......the repaired spots took the stain differently than the rest of the floor. Now I'd like to consider ceramic tile. The kitchen is L shaped with the small part of the L that comes off the main kitchen is only about 3' x 7' but a few feet from the wall, the floor dips approximately 1/8 th of an inch. Do I need to put down an entire plywood subfloor to level it and then top that with cement board before I tile? Is there any way around this? I got 3 estimates and the only one that noticed the dip included first checking each individual board of the hardwood floor and nailing down what needed to be nailed down then applying a plywood subfloor over the entire floor for leveling THEN putting down the cement board (of course this estimate is about $900 more than the others. Is this all necessary? Is there any way around this? Any suggestions/opinions would be appreciated.