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All trophies/achievements can be unlocked offline. However some spells that are in online only covenants require new game++ to be purchased from vendors. Abyssal covenant can be done offline obviously.
Currently Playing: Dark Souls 2, Tales of Symphonia Chronicles, Spyro 1-3 Last Completed: Tales of Xillia (8/10), Last Of Us (9/10)
But Sunlight Spear can only be gotten at the convenant? That means to get sunlight medals I have to go online or farm enemies with a very low drop rate, which is impossible because enemies stop spawning.
The guide I see shows that not all spells can be bought from that vendor.