A1: Ok in career mode, these are the ones I remember:

Durability/ Heal: beat an opponent with an overall 20 points higher than you and both of you having orange limb damage.
Steal Taunt: interupt your opponent while he's stealing your taunt.
Table Match: throw your opponents through 45 tables in your career.
Ladder Match: get 5 stars in a ladder match against Matt or Jeff Hardy.
Cage Match: win a steal cage match in under 1 minute by escaping.
Bleeding/ Hardcore Ressurection: make yourself and your opponents bleed 10 times in your career.

A2: Dirty Pin: Get a "5 Star" rank against three different opponents who have this ability.
Evasive Dodge: Win a Special match against two opponents.
Fan Favorite: Successfully taunt ten times in a match (must not have steal taunt).
Hammer Throw: Earn an ability within your first ten career matches, then get the "Sit In The Corner" award.
K.O.: Earn a "5 Star" rank against every competitor in a title path, not including the title match.
Kip-up: Win six championships.
Lock Pick: Face Y2J in a Singles match, and escape the Walls Of Jericho.
Move Theft: Defeat twenty different superstars.
Object Specialist (grab with object): Execute fifty object attacks in your career.
Outside Dives: Successfully complete twenty five dives in your career.
Referee Shield: Get five DQ losses, then win a championship match against a clean superstar.
Resiliency: Kick out of a pin at "2" while having two parts of red body damage.
Springboard: Win the Cruiserweight championship
Steal Taunt: Foil your opponent's attempt to steal your taunt (cannot have Fan Fave ability).
Submission: Attempt seven Struggle Submissions in one match, and then win.