As far as I can tell, the main grounds to contest it are along the lines of:
that it is invalid ie not witnessed, signed or incorrect information;
that the person was not of sound mind, or under duress;
that it doesn't meet the needs of legal dependents;
that there is another will.
I'm sure there'll be others and variances.
Whoever the other party is will most likely be keen to avoid the legal costs of defending a challenge, so maybe there's some room for mediation if you can make them believe you have a case?