Short Hop Aerial dodge his bombs. Shield Dash his arrows, and just be wary of his boomerang. No matter what, there's a very low chance of you completely dodging his boomerang without getting hit by something else or having your shield eaten up. Dash attack as he pulls out a bomb, but if you follow up, stay close and combo him. If you stay close and inactive, he can just SH and drop bomb right there and you'll have landed in the blast.
Don't try and shield grab him from behind unless he's just lagging badly from an attack. Chances are he'll just bair, and no one likes getting caught in TL's bairs.
Be wary of the arrows. TL might try and space a Nair, and while you're thinking he's caught in landing lag and try and dash in, he can actually use Bow Canceling to shoot an arrow to completely halt your approach. Even if your movement isn't completely thrown off, and you keep charging in, you still run the risk of running into his sword. He can also use Short Hopped Double Arrows to mimic Falco's Short Hop Double Lasers, so don't try and play mind games by trying to go immobile. Also, don't be fooled by arrows at midrange, that can just set him up for hyphen smash or dash attack (though you'll rarely see the latter). I also believe his arrows cancel out spin dash/charge. Not sure about that or his boomerang, though.
If you need the KO, the only way you're getting a star KO is from a utilt at around 140%. If you're going for uair>spring>uair, you better be quick or get daired. Otherwise, you'll have to aim for the blast lines on the side. Before he pulls out a projectile to cover his way back, you've got a shot to gimp him with Homing Attack. Other than that, his recovery is rediculous, so force him to come in low and instant edgegrab at the last second. Even if he comes up above the ledge afterwards, you can clock in a quick attack as he lands, possibly even smashing him afterwards.
That's my perspective not from knowing the matchup, but from knowing what I do as Toon Link.