Can my team beat Rigor Mortex?

Possibly. You haven't given any stats so I can't say for sure. You might get Koed in 2 turns or beat him easy as. You want your healer to have 250+MP and all your monsters will probably need 400+HP and 400+defence(metals wont need 400Hp). Your attacker should have maybe 500+ attack and should also have higher defence than the rest of your monsters.The dragon slime should probably be synthesised into something stronger. Maybe mix it with a yabby to make a beetleboy.
If your team is all +15 or something ridiculous like that then you probably should have beaten him ages ago but it doesn't seem like you have synthesised that much.
My team consisted of a physical attacker, an all-round attacker(magic and physical but I only used physical) and a healer
The physical attacker was a dullahan. He had about 600HP 600 defence and 500-600Attack.
The all round attacker was a killing machine. He had about 600Hp 500defence and a little less attack than the dullahan
The healer was a demon-at-arms. He had Uber Healer Maxed, 450Hp, 250-300MP and 400-500 defence
I used the basic tactics-Attack and heal when I needed. I didn't use any yggdrasil leaves or anything

If I were you I would use a psaro and a great dragon