Swim checks for getting to the egg chamber. Using better of two rolls due to hex:

Round 1 (1d20+4)[14] (1d20+4)[15]
Round 2 (1d20+4)[23] (1d20+4)[23]
Round 3 (1d20+4)[24] (1d20+4)[7]
Round 4 (1d20+4)[6] (1d20+4)[15]
Round 5 (1d20+4)[23] (1d20+4)[6]
Round 6 (1d20+4)[15] (1d20+4)[22]
Round 7 (1d20+4)[9] (1d20+4)[23]
Round 8 (1d20+4)[12] (1d20+4)[6]
Round 9 (1d20+4)[6] (1d20+4)[20]
Round 10 (1d20+4)[24] (1d20+4)[23]
Round 11 (1d20+4)[15] (1d20+4)[13]
Round 12 (1d20+4)[24] (1d20+4)[8]
Round 13 (1d20+4)[21] (1d20+4)[19]
Round 14 (1d20+4)[10] (1d20+4)[17]
Round 15 (1d20+4)[7] (1d20+4)[14]
Round 16 (1d20+4)[10] (1d20+4)[16]
Round 17 (1d20+4)[24] (1d20+4)[8]
Round 18 (1d20+4)[15] (1d20+4)[24]
Round 19 (1d20+4)[11] (1d20+4)[16]
Round 20 (1d20+4)[15] (1d20+4)[10]
Round 21 (1d20+4)[17] (1d20+4)[5]
Round 22 (1d20+4)[7] (1d20+4)[21]
Round 23 (1d20+4)[23] (1d20+4)[15]
Round 24 (1d20+4)[22] (1d20+4)[5]

If I still haven't made it across by the end of this string of rolls I start to drown and need to roll more.